Suma
Posted: Sat Nov 08, 2008 9:41 am
Calculati suma : \( S=\frac{201}{2}+\frac{601}{6}+\frac{1201}{12}+...+\frac{9001}{90} \)
\( S=\frac{200}{2}+\frac{600}{6}+\frac{1200}{12}+\ldots+\frac{9000}{90}+\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\ldots+\frac{1}{9\cdot 10} \)
\( \Longleftrightarrow\ S=100\cdot 9+1-\frac 12+\frac 12-\frac 13+\ldots+\frac 19-\frac{1}{10}=900+\frac{9}{10}=900,9 \)