In this problem random variable is L
L can be 1,2,..............
P{L = 1} = 1/2
P{L = 2} = 1/4
P{L = 3} = 18
H{L} = 1/2log21/(1/2) + 1/4log21/(1/8) + ..... = 0 + 1 x 1/2 + 2 x 1/4 + 3 x 1/8 + ...
[Arithmatic gemometric series summation]
= 2/(1 - 1/2) + (1/2 x 1)/(1 - 1/2)2 = 2