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## Homework Statement

Figuring out an infinite sum question for the kid I tutor... it's late and my brain's not functioning well. I think I'm overcomplicating the question, but I can't figure it out.

The the sum of the following infinite series:

S = 1+3x+5x^2+...

## Homework Equations

## The Attempt at a Solution

I got that tn = [tex](2n-1)x^{n-1}[/tex]

Which means the sum is

[tex]\Sigma (2n-1)x^{n-1}=2\Sigma nx^{n-1} - \Sigma x^{n-1} = 2\Sigma nx^{n-1} - \frac{1}{1-x}[/tex]

And here is where I get stuck...