Question

Tính nhanh

A=2/6+2/12+2/20+2/30+...+2/10100

Answer 1

\(A=\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+\dfrac{2}{30}+...+\dfrac{2}{10100}\)

\(A=2\times\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{100\times101}\right)\)

\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{100}-\dfrac{1}{101}\right)\)

\(A=2\times\left(\dfrac{1}{2}-\dfrac{1}{101}\right)\)

\(A=2\times\dfrac{99}{202}\)

\(A=\dfrac{99}{101}\)