Question

C= 1/3+1/6+1/10+...+1/5050

Mọi người giúp em vs ạ

Answer 1

\(C=\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{5050}\)

\(=2\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{10100}\right)\)

\(=2\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{100\cdot101}\right)\)

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

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

\(=2\cdot\dfrac{99}{202}=\dfrac{99}{101}\)