How do I figure out if the series from 3 to inf of ((1/2)^(n+1))((2/3)^n) converges or diverges? I think it has something to do with the value of r, but this problem is confusing me because it is written as a product.
((1/2)^(n+1))((2/3)^n)
= (1/2)(1/2)^n (2/3)^n
= 1/2 (1/3)^n
This is just a geometric series with
a = (1/2)(1/3)^3 = 1/54
r = 1/3