Finding the sum of k²x^k for |x| < 1

Eismc[] · Nov 21, 2005

Hello everyone,

does someone know what the value of [SUM (k from 0 to infinity) k²(x^k)] (with |x| < 1) is? I couldn't find it anywhere. :-( Are there any good online databases for such things?

Many thanks in advance!

mathman · Nov 21, 2005

Starting with sum x^k =1/(1-x), you can easily derive what you want faster than trying to look it up. Take the derivative of both sides, mutiply both sides by x, repeat both steps, you will end up with what you are looking for.

Finding the sum of k²x^k for |x| < 1

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