Question

\(\dfrac{7}{110}\)+\(\dfrac{7}{132}\)+\(\dfrac{7}{156}\)+...+\(\dfrac{7}{4830}\)

Đề: Tính tổng

Help mee! Gấp ạ!!!

Answer 1

\(\dfrac{7}{110}+\dfrac{7}{132}+\dfrac{7}{156}+...+\dfrac{7}{4830}\)

\(=\dfrac{7}{10\cdot11}+\dfrac{7}{11\cdot12}+\dfrac{7}{12\cdot13}+...+\dfrac{7}{69\cdot70}\)

\(=7\left(\dfrac{1}{10}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{13}+...+\dfrac{1}{69}-\dfrac{1}{70}\right)\)

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

\(=7\cdot\dfrac{3}{35}=\dfrac{3}{5}\)