Convergence of series

Eismc[]

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

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.

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Eismc[]	Convergence of series Tweet 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 Recognitions: Science Advisor	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.