(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to find a closed form formula for:

[tex]x+2x^2+3x^3+4x^4+\ldots[/tex]

I know that this can be written as:

[tex]\sum_{n=1}^{\infty}nx^n[/tex]

but I would like to have a closed formula for this.

The formula for an infinite geometric series is:

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

Which is somewhat close but the series in question is not exactly geometric.

How do I go about doing this?

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# Homework Help: Help on infinite series

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