Question

6/ 4 x 7 + 6/7 x 10 + 6/10 x 13 + ..... + 6/82 x 85

Answer 1

Giải:

Đặt \(A=\dfrac{6}{4.7}+\dfrac{6}{7.10}+\dfrac{6}{10.13}+...+\dfrac{6}{82.85}\)

\(\dfrac{1}{2}A=\dfrac{3}{4.7}+\dfrac{3}{7.10}+\dfrac{3}{10.13}+...+\dfrac{3}{82.85}\)

\(\dfrac{1}{2}A=\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+...+\dfrac{1}{82}-\dfrac{1}{85}\)

\(\dfrac{1}{2}A=\dfrac{1}{4}-\dfrac{1}{85}\)

\(\dfrac{1}{2}A=\dfrac{81}{340}\)

\(\Rightarrow A=\dfrac{81}{340}:\dfrac{1}{2}\)

\(A=\dfrac{81}{170}\)