Question

\(A=\dfrac{1}{1x3}+\dfrac{1}{3x5}+\dfrac{1}{5x7}+...+\dfrac{1}{49x51}\)

 

Answer 1

`A=1/[1xx3]+1/[3xx5]+1/[5xx7]+...+1/[49xx51]`

`A=1/2xx(2/[1xx3]+2/[3xx5]+2/[5xx7]+...+2/[49xx51])`

`A=1/2xx(1-1/3+1/3-1/5+1/5-1/7+...+1/49-1/51)`

`A=1/2xx(1-1/51)`

`A=1/2xx50/51`

`A=25/51`

Answer 2

\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{49\cdot51}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{49}-\dfrac{1}{51}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{50}{51}=\dfrac{25}{51}\)