# Series help

1. Sep 4, 2007

### fsm

1. The problem statement, all variables and given/known data
$$\sum (1+2^n)/3^n$$

Find its sum

2. Relevant equations

3. The attempt at a solution
I don't know how to figure this one out. I took the limit and it was zero so I know it converges. I dont know where to start on this one. The answer is 5/2.

2. Sep 4, 2007

### TMFKAN64

Write this as the sum of two summations.

3. Sep 5, 2007

### HallsofIvy

Staff Emeritus
More precisely, the sum of two geometric series.

4. Sep 6, 2007

### Gib Z

And just because the the terms approach zero, the series always convergent. Think of the harmonic series.

5. Sep 6, 2007

### HallsofIvy

Staff Emeritus
Typo? I'm quite sure Gib Z meant "just because the terms approach zero, the series is not always convergent". Yes, this particular series converges but your statement " I took the limit (of the sequence of terms) and it was zero so I know it converges" does not follow.
The fact that the limit of the sequence of terms goes to zero is necessary for convergence but not sufficient.

6. Sep 6, 2007

### Gib Z

Typo indeed :( Was in a rush for that post lol.