https://gateoverflow.in/20011/tifr2011-a-6

For more such problems: https://www.codechef.com/wiki/tutorial-expectation

X= No of times coin is tossed.

X=2,3,4..

X 2 3 4 5 .........

P[X=x] (1/2)^2 (1/2)^3 (1/2)^4 (1/2)^5 .........

E[x] = 2*(1/2)^2 + 3*(1/2)^3 + 4*(1/2)^4 + 5*(1/2)^5 + .....

This is an AGP. On solving this gives

E[x] = 1.5