Tính nhanh

A= 1/1x2x3 + 1/2x3x4 + 1/3x4x5 +...+ 1/98x99x100

Đáp án `+`Giải thích các bước giải:

 `A` `=` `1/1` x `2` x `3` `+` `1/2` x `3` x `4` `+` `1/3` x `4` x `5` `+`.......`+` `1/98` x `99` x `100`

\(A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{100-98}{98.99.100}\)

\(A=\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right):2\)

\(A=\left(\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{12}-\dfrac{1}{20}+...+\dfrac{1}{9702}-\dfrac{1}{990}\right):2\)

\(A=\left(\dfrac{1}{2}-\dfrac{1}{990}\right):2\)

\(A=\dfrac{4949}{9900}:2\)

\(A=\dfrac{4949}{19800}\)