Sum of Geometric Series: Ʃ(3→∞) 3(.4)^(n+2)

[Rapier]

Homework Statement

Find the sum of Ʃ(3→∞) 3(.4)^(n+2)

Homework Equations

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

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.

 

[gb7nash]

First off, what's the first term of the series? (a is not 3)

Next, r is what you multiply by to get from one term to another. Write out the first few terms of the series. What do you multiply by to get from the first term to the second?

Now that you have a and r, you can calculate the sum.

 

[Rapier]

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!