# Sum to the infinity of a series

1. Jul 15, 2012

### justwild

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

to find the value of $\sum$ over n=1 to ∞ of [1/{1+(n-1)2}](1/3)$^{2+(n-1)2}$

2. Relevant equations

3. The attempt at a solution
I have tried to solve in the way the arithmetico-geometric series are solved and tried to bring it in the form of the expansion of ln(1+y), because the answer has logarithmic term in it.

2. Jul 15, 2012

### Curious3141

Hints:

Get rid of the (n-1) by starting the sum off from n = 0, that'll make things clearer.

Observe that ${(\frac{1}{3})}^{2 + 2n} =\frac{1}{3}.{(\frac{1}{3})}^{2n + 1}$

What's $\int_0^x t^{2n} dt$?