Question

Tính S = 7+ 7/3+7/6+7/10+7/15+7/21+7/28+7/36+7/45+7/55
 

Answer 1

\(S=7\left(1+\dfrac{1}{3}+\dfrac{1}{6}+...+\dfrac{1}{55}\right)\)

\(=7\left(\dfrac{2}{2}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{110}\right)\)

\(=14\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{110}\right)\)

\(=14\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\right)\)

\(=14\cdot\dfrac{10}{11}=\dfrac{140}{11}\)