Find the Sum

1. The problem statement, all variables and given/known data

Find the sum of Ʃ(3→∞) 3(.4)^(n+2)

2. Relevant equations

Sum of Geometric Series = ao/(1 - r), ao=3, r = .4 = 2/5

3. The attempt at a solution

I thought that I could use the definition of the sum of a geometric series (above) to determine the sum of this equation. So 3/(1-.4) = 5. I believe that somewhere I need to account for the difference in taking the sum of the series from 1 (like I normally would) and 5 (series starts at 3 and the ratio is n+2). But I'm not sure how I do that.

 

Ah! The first term of this series would be .03072.

I can only use a0 = 3 if I started this series at n=1. I have to recalculate my a0 term given the changed starting point.

This series converges to 32/625 or .0512.

Thanks!