- #1
Somefantastik
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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?