Question

\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}+\frac{1}{156}\)

Tính tổng S.

Answer 1

\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{132}+\frac{1}{156}\)

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{11.12}+\frac{1}{12.13}\)

\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}\)

\(S=\frac{1}{1}-\frac{1}{13}\)

\(S=\frac{12}{13}\)

Answer 2

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{12.13}\)

    \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{12}-\frac{1}{13}\)

    \(=1-\frac{1}{13}\)

    \(=\frac{12}{13}\)