Question

[Nguyễn Hà Linh]

B=\(\dfrac{-1}{3}\)+ \(\dfrac{-1}{3.5}\)+ \(\dfrac{-1}{5.7}\)+ \(\dfrac{-1}{7.9}\) +... + \(\dfrac{-1}{99.101}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

\(B=-\dfrac{1}{2}\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\)

\(=\dfrac{-1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{-1}{2}\cdot\dfrac{100}{101}=-\dfrac{50}{101}\)