Question

Value of 1/1×3+1/1×3+1/5×7+........+1/97×99 is

Answer 1

Answer:

49 / 99

Step-by-step explanation:

The n-th term of this series is

$\displaystyle\frac1{(2n-1)(2n+1)}=\frac12\left(\frac{1}{2n-1}-\frac{1}{2n+1}\right)$

Therefore the given sum is

$\displaystyle\frac12\left(\left(\frac11-\frac13\right)+\left(\frac13-\frac15\right)+\left(\frac15-\frac17\right)+\dots+\left(\frac1{97}-\frac1{99}\right)\right)\\\\=\frac12\left(1-\frac1{99}\right)\\\\=\frac12\times\frac{98}{99}\\\\=\frac{49}{99}$