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## Homework Statement

find the sum for

[tex]\sum_{k=1}^{\infty} kx^{k} [/tex]

## Homework Equations

[tex]\sum_{k=0}^{\infty} x^{k} = \frac{1}{1-x}; -1 < x < 1 [/tex]

## The Attempt at a Solution

[tex] \sum_{k=1}^{\infty} kx^{k} = \sum_{n=0}^{\infty}(n+1)x^{n+1} = x\sum_{n=0}^{\infty} (n+1)x^{n} = x \frac{d}{dx} \sum_{n=0}^{\infty}x^{n+1}[/tex]

I'm not sure how to proceed; thoughts?