Suma

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alex2008
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Suma

Post by alex2008 »

Calculati suma : \( S=\frac{201}{2}+\frac{601}{6}+\frac{1201}{12}+...+\frac{9001}{90} \)
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Mateescu Constantin
Newton
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Post by Mateescu Constantin »

\( S=\frac{200}{2}+\frac{600}{6}+\frac{1200}{12}+\ldots+\frac{9000}{90}+\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\ldots+\frac{1}{9\cdot 10} \)

\( \Longleftrightarrow\ S=100\cdot 9+1-\frac 12+\frac 12-\frac 13+\ldots+\frac 19-\frac{1}{10}=900+\frac{9}{10}=900,9 \)
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