Question

tính nhanh:2/11x13+2/13x15+2/15x17+...+2/97x99

 

Answer 1

`2/(11x13) + 2/(13xx15) + 2/(15xx17) + ... + 2/(97xx99)`

`= 1/11 - 1/13 + 1/13 - 1/15 + 1/15 - 1/17 + ... + 1/97 - 1/99`

`= 1/11 - 1/99`

`= 8/99`

Answer 2

\(=\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{97}-\dfrac{1}{99}=\dfrac{1}{11}-\dfrac{1}{99}=\dfrac{8}{99}\)

Answer 3

Đặt \(A=\dfrac{2}{11\times13}+\dfrac{2}{13\times15}+...+\dfrac{2}{97\times99}\)

\(\Rightarrow A=\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{97}-\dfrac{1}{99}\)

\(\Rightarrow A=\dfrac{1}{11}-\dfrac{1}{99}\)

\(\Rightarrow A=\dfrac{9}{99}-\dfrac{1}{99}=\dfrac{8}{99}\)