Question

tính tổng S=1/6+1/12+1/20+..........+1/600+1/650

Answer 1

\(S=\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{600}+\dfrac{1}{650}\)

\(=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{24\cdot25}+\dfrac{1}{25\cdot26}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{26}\)

\(=\dfrac{1}{2}-\dfrac{1}{26}=\dfrac{13-1}{26}=\dfrac{12}{26}=\dfrac{6}{13}\)