Question

[pham quoc hao]

\(\frac{7}{10.11}\)+\(\frac{7}{11.12}\)+\(\frac{7}{12.13}\)+...+\(\frac{7}{69.70}\)

Tính tổng sau

Answer 1

[Thắng Nguyễn]

\(=7\left(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{69.70}\right)\)

\(=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(=7\times\frac{6}{70}\)

\(=\frac{6}{10}=\frac{3}{5}\)

Answer 2

[Kalluto Zoldyck]

Gọi tổng trên là A

A = 7/10.11 + 7/11.12 +.....+ 7/69.70

A = 7(1/10.11 + 1/11.12 +.....+ 1/69.70)

A =7( 1/10 - 1/11 + 1/11 - 1/12 +.....+ 1/69 - 1/70)

A = 7( 1/10 - 1/70)

A = 7 . 3/35

A = 21/35