Question

Bài 6: Tính các tổng sau:

A= \(\dfrac{7}{10.11}\)+\(\dfrac{7}{11.12}\)+\(\dfrac{7}{12.13}\)+...+\(\dfrac{7}{69.70}\)

B= \(\dfrac{1}{25.27}\)+\(\dfrac{1}{27.29}\)+\(\dfrac{1}{29.31}\)+...+\(\dfrac{1}{73.75}\)

Answer 1

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

\(=7\left(\dfrac{1}{10}-\dfrac{1}{70}\right)=\dfrac{7.60}{700}=\dfrac{420}{700}=\dfrac{3}{5}\)

\(B=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}-\dfrac{1}{29}+...+\dfrac{1}{73}-\dfrac{1}{75}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{25}-\dfrac{1}{75}\right)=\dfrac{1}{75}\)