Evaluate Σ from n=1 to infinity of 3/2^n-1

Question

a) 12
b) 6
c) 3
d) 0 ----> my answer. Can you check for me, please? Thanks in advance

Answer 1

you just have a geometric series where
a = 3
r = 1/2
S = 3/(1 - 1/2) = 6

The nth term converges to zero, but the sum does not