# Homework Help: Finding sum of convergent series.

1. Nov 16, 2012

### peripatein

Hi,

I have determined, correctly I believe, that the following series converges:
1/[(3n-2)(3n+1)]
Now I am asked to determine its sum. I have tried separating it into two subseries, but each time got a p-series with p=1, hence to no avail.
The answer should be 1/3, but how may it be arrived at?

2. Nov 16, 2012

### Staff: Mentor

I would rewrite 1/[(3n-2)(3n+1)] as the sum of two fractions, using partial fraction decomposition. When you have done that, expand the new series. You'll probably find that the series is a telescoping one.

3. Nov 16, 2012

### Curious3141

Partial fractions, following which you get a very simple telescoping series. Write out the first few terms of each.

4. Nov 16, 2012

### Zondrina

Last edited: Nov 16, 2012
5. Nov 16, 2012

### Staff: Mentor

The OP has already determined that the series converges. Now he/she needs to determine its sum.

6. Nov 16, 2012

### peripatein

Thanks!
How may I know whether the series ((-1)^n)[cos (3^n)x]^3/(3^n) converges/diverges?Should I use the Leibnitz Criterion?
It is stated that (cos a)^3 = (1/4)(3cos a + cos 3a)

7. Nov 16, 2012

### SammyS

Staff Emeritus
I suggest starting a new thread for this.