Question

Giair giúp mk bài toán bên dưới ạ

Answer 1

\(A=\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+...+\dfrac{1}{\left(x+2013\right)\left(x+2014\right)}\)

\(A=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+...+\dfrac{1}{x+2013}-\dfrac{1}{x+2014}\)

\(A=\dfrac{1}{x}-\dfrac{1}{x+2014}=\dfrac{2014}{x\left(x+2014\right)}\)

Answer 2

Answer 3

Answer 4

Answer 5

@Trần Trung Nguyên @Nguyễn Việt Lâm