Question

Tính tổng sau:

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

Answer 1

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

= \(7\left(\dfrac{1}{10.11}+\dfrac{1}{11.12}+\dfrac{1}{12.13}+...+\dfrac{1}{69.70}\right)\)

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

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

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

= \(7.\dfrac{6}{70}\)

= \(\dfrac{3}{5}\)