# $eq=\frac{1}{\sqrt{1} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{7}} + .....+ ....$

India VK
42 Points
8 years ago

Rationalize each term

eq = 1/2 (root 3 - root 1) + 1/2 (root 5 - root 3) + 1/2 (root 7 - root 5) + .... + 1/2 (root 2n+1 - root 2n-1)

This is a telescoping series. Easy to find the sum.