infinite series problem?

Question

What is the value of sum from 1 to inf of (2^(n+1))/(3^n).

I keep getting 6 but the answer is 4

Answer 1

This is a geometric series with first term a = 2^2 / 3^1 = 4/3
and ratio r = 2/3
so the series sum is S = a / (1 - r) = (4/3) / (1/3) = 4.