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Convergence of series

  1. Nov 21, 2005 #1
    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!
  2. jcsd
  3. Nov 21, 2005 #2


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    Gold Member

    Starting with sum xk =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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