Thursday 31 July 2014

sequences and series - How can I evaluate $sum_{n=1}^{infty} n^{3}x^{n-1}$

How do i evaluate :



$$\sum_{n=1}^{\infty} n^{3}x^{n-1}$$




The answer is supposed to be: (according to wolfram alpha)



$$ \frac{x^2+4x+1}{(x-1)^4} $$



I have only learned to to this for simpler geometric sums.

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