Question

Answer 1

Đặt \(P=\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}+\dfrac{1}{11\times13}\)

`=>`\(2P=\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}\)

`=>`\(2P=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\)

`=>`\(2P=\dfrac{1}{3}-\dfrac{1}{13}\)

`=>`\(2P=\dfrac{10}{39}\)

`=>`\(P=\dfrac{5}{39}\)

Answer 2

Đặt `A=1/(3xx5)+1/(5xx7)+1/(7xx9)+1/(9xx11)+1/(11xx13)`

`=> 2A=2/(3xx5)+2/(5xx7)+2/(7xx9)+2/(9xx11)+2/(11xx13)`

`=> 2A=1/3-1/5+1/5-1/7+...+1/11-1/13`

`=> 2A=1/3-1/13`

`=> 2A=10/39`

 

 

Answer 3

\(\dfrac{10}{39}\)