This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) (format=latex 2009.7.6) 21 APR 2010 15:28 entering extended mode %&-line parsing enabled. **varie.tex (./varie.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, loaded. ! Undefined control sequence. l.2 \section {Proposizioni varie} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.2 \section{P roposizioni varie} You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no P in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no z in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no v in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no e in font nullfont! ! LaTeX Error: Environment prop undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.3 \begin{prop} \label{sommapriminnumeri} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Undefined control sequence. l.4 \eal {&\sum_{i=1}^n i =\frac{n(n+1)}{2}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.4 \eal{& \sum_{i=1}^n i =\frac{n(n+1)}{2}} I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Missing $ inserted. $ l.4 \eal{&\sum _{i=1}^n i =\frac{n(n+1)}{2}} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 4. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 4. ! Extra }, or forgotten $. l.4 \eal{&\sum_{i=1}^n i =\frac{n(n+1)}{2}} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{prop}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.5 \end{prop} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.5 \end{prop} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.5 \end{prop} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment proof undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.6 \begin{proof} Your command was ignored. Type I to replace it with another command, or to continue without it. Missing character: There is no S in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.8 \eal {&\sum_{i=1}^n i =1+2+3+\dots+(n-3)+ (n-2)+(n-1)+n= The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.8 \eal{& \sum_{i=1}^n i =1+2+3+\dots+(n-3)+ (n-2)+(n-1)+n= I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Missing $ inserted. $ l.8 \eal{&\sum _{i=1}^n i =1+2+3+\dots+(n-3)+ (n-2)+(n-1)+n= I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Misplaced alignment tab character &. & l.10 & = I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.11 (\ubrace {n+n+n+\dots+n}{(n-1)/2\T{ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.11 (\ubrace{n+n+n+\dots+n}{(n-1)/2\T { The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Extra }, or forgotten $. l.13 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. Missing character: There is no n in font nullfont! ! Undefined control sequence. l.15 \eal {&\sum_{i=1}^n i =n+\sum_{i=1}^{n-1} i \ubrace{=}{n-1\T{ dispari}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.15 \eal{& \sum_{i=1}^n i =n+\sum_{i=1}^{n-1} i \ubrace{=}{n-1\T{ dispari}} I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.15 ...um_{i=1}^n i =n+\sum_{i=1}^{n-1} i \ubrace {=}{n-1\T{ dispari}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.15 ...n i =n+\sum_{i=1}^{n-1} i \ubrace{=}{n-1\T { dispari}} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{proof}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.18 \end{proof} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.18 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.18 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. Overfull \hbox (20.0pt too wide) in paragraph at lines 2--19 [] [] Overfull \hbox (39.67719pt too wide) in paragraph at lines 2--19 [][] \OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = [] Overfull \hbox (28.66173pt too wide) in paragraph at lines 2--19 []$ [] Overfull \hbox (6.00235pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n$ [] Overfull \hbox (39.67719pt too wide) in paragraph at lines 2--19 [][] \OML/cmm/m/it/10 i \OT1/cmr/m/n/10 = [] Overfull \hbox (12.77782pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 1 + [] Overfull \hbox (12.77782pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 2 + [] Overfull \hbox (12.77782pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 3 + [] Overfull \hbox (19.44441pt too wide) in paragraph at lines 2--19 [] \OT1/cmr/m/n/10 + [] Overfull \hbox (17.66905pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (16.66672pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 3) + [] Overfull \hbox (17.66905pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (16.66672pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 2) + [] Overfull \hbox (17.66905pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 (\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (16.66672pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 1) + [] Overfull \hbox (16.55786pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OT1/cmr/m/n/10 = [] Overfull \hbox (18.75005pt too wide) in paragraph at lines 2--19 []\OT1/cmr/m/n/10 1 + [] Overfull \hbox (17.36118pt too wide) in paragraph at lines 2--19 []\OT1/cmr/m/n/10 2 + [] Overfull \hbox (16.66672pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 (3 + [] Overfull \hbox (19.44441pt too wide) in paragraph at lines 2--19 [] \OT1/cmr/m/n/10 + [] Overfull \hbox (13.78015pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (16.66672pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 3) + [] Overfull \hbox (13.78015pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (17.36118pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 2[] + [] Overfull \hbox (13.78015pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^@ [] Overfull \hbox (18.75005pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 1[] + [] Overfull \hbox (16.55786pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OT1/cmr/m/n/10 = [] Overfull \hbox (7.7778pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 = [] Overfull \hbox (162.62369pt too wide) in paragraph at lines 2--19 \OT1/cmr/m/n/10 ([][]) + [] Overfull \hbox (16.55786pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OT1/cmr/m/n/10 = [] Overfull \hbox (31.35962pt too wide) in paragraph at lines 2--19 []\OML/cmm/m/it/10 n \OT1/cmr/m/n/10 + [] Overfull \hbox (16.55786pt too wide) in paragraph at lines 2--19 \OML/cmm/m/it/10 n \OT1/cmr/m/n/10 = [] Overfull \hbox (71.59526pt too wide) in paragraph at lines 2--19 []\OML/cmm/m/it/10 Se$$e[]pari \OT1/cmr/m/n/10 : [] Overfull \hbox (281.41777pt too wide) in paragraph at lines 2--19 []$ [] ! LaTeX Error: Environment prop undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.20 \begin{prop} \label{sommaquadrati} Your command was ignored. Type I to replace it with another command, or to continue without it. ! LaTeX Error: Missing \begin{document}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.21 S omma quadrati: You're in trouble here. Try typing to proceed. If that doesn't work, type X to quit. Missing character: There is no S in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no q in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no d in font nullfont! Missing character: There is no r in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.22 \eal {&\sumin i^2=\frac{2n^3+3n^2+n}{6} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.22 \eal{& \sumin i^2=\frac{2n^3+3n^2+n}{6} I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.22 \eal{&\sumin i^2=\frac{2n^3+3n^2+n}{6} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. Missing character: There is no i in font nullfont! ! Missing $ inserted. $ l.22 \eal{&\sumin i^ 2=\frac{2n^3+3n^2+n}{6} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. l.23 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! LaTeX Error: \begin{document} ended by \end{prop}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.24 \end{prop} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.24 \end{prop} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.24 \end{prop} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! LaTeX Error: Environment proof undefined. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.25 \begin{proof} Your command was ignored. Type I to replace it with another command, or to continue without it. Missing character: There is no D in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no t in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no u in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no c in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no s in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no e in font nullfont! Missing character: There is no , in font nullfont! Missing character: There is no p in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no n in font nullfont! Missing character: There is no i in font nullfont! Missing character: There is no a in font nullfont! Missing character: There is no m in font nullfont! Missing character: There is no o in font nullfont! Missing character: There is no : in font nullfont! ! Undefined control sequence. l.28 \eal {&\D a_i = a_{i+1}-a_i} The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.28 \eal{& \D a_i = a_{i+1}-a_i} I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Missing $ inserted. $ l.28 \eal{&\D a_i = a_{i+1}-a_i} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Extra }, or forgotten $. \D ->{\Delta } l.28 \eal{&\D a_i = a_{i+1}-a_i} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Extra }, or forgotten $. l.28 \eal{&\D a_i = a_{i+1}-a_i} I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Undefined control sequence. l.30 \eal {&\D i^3 =(i+1)^3-i^3=1+3i^2+3i\\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. l.30 \eal{& \D i^3 =(i+1)^3-i^3=1+3i^2+3i\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. & l.31 & 3i^2=\D i^3 -3i-1\\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Misplaced alignment tab character &. & l.32 & 3\sumin i^2 = \sumin \pton{\D i^3 -3i-1} = \\ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.32 &3\sumin i^2 = \sumin \pton{\D i^3 -3i-1} = \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.32 &3\sumin i^2 = \sumin \pton{\D i^3 -3i-1} = \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.32 &3\sumin i^2 = \sumin \pton {\D i^3 -3i-1} = \\ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. & l.33 & \qq \sumin \D i^3 = \sumin (i+1)^3-i^3 = 2^3-1^3 + 3^3-2^3 + \dots + I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.33 &\qq \sumin \D i^3 = \sumin (i+1)^3-i^3 = 2^3-1^3 + 3^3-2^3 + \dots + The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.33 &\qq \sumin \D i^3 = \sumin (i+1)^3-i^3 = 2^3-1^3 + 3^3-2^3 + \dots + The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.33 &\qq \sumin \D i^3 = \sumin (i+1)^3-i^3 = 2^3-1^3 + 3^3-2^3 + \dots + The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. & l.35 & = (n+1)^3-1^3 -3\sumin i - \sumin 1 I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.35 &= (n+1)^3-1^3 -3\sumin i - \sumin 1 The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.35 &= (n+1)^3-1^3 -3\sumin i - \sumin 1 The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.36 \ubrace {=}{\see{sommapriminnumeri}} (n+1)^3-1^3 The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Undefined control sequence. l.36 \ubrace{=}{\see {sommapriminnumeri}} (n+1)^3-1^3 The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! Misplaced alignment tab character &. & l.38 & \sumin i^2 = \frac{ I can't figure out why you would want to use a tab mark here. If you just want an ampersand, the remedy is simple: Just type `I\&' now. But if some right brace up above has ended a previous alignment prematurely, you're probably due for more error messages, and you might try typing `S' now just to see what is salvageable. ! Undefined control sequence. l.38 &\sumin i^2 = \frac{ The control sequence at the end of the top line of your error message was never \def'ed. If you have misspelled it (e.g., `\hobx'), type `I' and the correct spelling (e.g., `I\hbox'). Otherwise just continue, and I'll forget about whatever was undefined. ! LaTeX Error: \begin{document} ended by \end{proof}. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.45 \end{proof} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ l.45 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.45 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Missing } inserted. } l.45 \end{proof} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ) ! Emergency stop. <*> varie.tex *** (job aborted, no legal \end found) Here is how much of TeX's memory you used: 11 strings out of 95087 183 string characters out of 1183279 48034 words of memory out of 1500000 3283 multiletter control sequences out of 10000+50000 3640 words of font info for 14 fonts, out of 1200000 for 2000 28 hyphenation exceptions out of 8191 18i,6n,12p,83b,62s stack positions out of 5000i,500n,6000p,200000b,5000s No pages of output.