sum of series of 1+2/4+3/8+4/16+..........can u please elaborate and explain it.i didnt get the solution which is already there in course..

Let S = 1 + 2/4 + 3/8 + 4/16 +...
S - 1 = 2/4 + 3/8 + 4/16 + ...
(S-1)/2 = 2/8 + 3/16 + 4/32 +...
(S - 1) - (S-1)/2 = 2/4 + 1/8 + 1/16 + 1/32 +...
= 2/4 + (1/8)/(1 - 1/2) = 1/2 + 1/4 = 3/4
So, (S-1)/2 = 3/4
=> S - 1 = 3/2
S = 5/2

How to find nth term for this series?

Download Progressions and Series formulas pdf for CAT, and learn various techniques to solve this kind of problems.