31 lines
706 B
TeX
31 lines
706 B
TeX
\documentclass[a4paper,12pt]{article}
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\usepackage[utf8]{inputenc}
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\usepackage{amsmath, amssymb, mathtools}
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\title{Gauss ha 8 anni, solzuione}
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\author{Jacopo Basso Ricci}
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\date{\today}
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\begin{document}
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\maketitle
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Scriviamo la somma $S$ in modo intelligente:
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\vspace{10px}
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\begin{tabular}{c c c c c c c c c}
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&$S = $&$ 1 +$&$ 2 + $&$ 3 +$&$ \dots +$&$ 98 + $&$ 99 + $&$ 100$\\
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$+$&$S = $&$ 100 + $&$ 99 + $&$ 98 + $&$ \dots +$&$ 3 + $&$ 2 + $&$ 1$\\[0.5ex]
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\hline
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&$2S =$&$101 + $&$101 + $&$101 + $&$ \dots + $&$101 + $&$101 + $&$101$
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\end{tabular}
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\vspace{5mm}
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Notiamo quindi che
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\[ 2S = 101 * 100\]
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\[ S = \frac{101 * 100}{2} = 101 * 50 = 5050 \]
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Soluzione \boxed{ S = 5050}
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\end{document}
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