Question

Tính: \(B=\dfrac{-1}{99}+\dfrac{1}{99.98}-\dfrac{1}{98.97}-...-\dfrac{1}{2.1}\)

_{Giải chi tiết dùm mình nhe. Thanks}

Answer 1

\(B=\dfrac{-1}{99}+\dfrac{1}{99\cdot98}-\dfrac{1}{98\cdot97}-...-\dfrac{1}{2\cdot1}\)

\(=\dfrac{-1}{99}+\dfrac{1}{98\cdot99}-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{97\cdot98}\right)\)

\(=-\dfrac{2}{99}+\dfrac{1}{98}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{97}-\dfrac{1}{98}\right)\)

\(=-\dfrac{2}{99}+\dfrac{1}{98}-\dfrac{97}{98}=\dfrac{-2}{99}-\dfrac{23}{49}=\dfrac{-2375}{4851}\)