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Find formula for f[x] whose expansion in powers of x is

  1. Sep 26, 2011 #1
    I am trying to find formula for f[x] whose expansion in powers of x is:
    x + 2^2 x^2 + 3^2 x^3 + 4^2 x^4 + ... + k^2 x^k + ...

    I know that this is a variation on x/(1-x). I also know that x/(1-x)^2 yields expansion in power of x = kx^k. I cannot figure out the manipulation which would give the expansion k^2x^k.

    Any help is appreciated
  2. jcsd
  3. Sep 26, 2011 #2


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    Well, if I had a series expansion that gave me terms kxk and I differentiated it that would give k2xk-1 and if I multiplied by x ...
  4. Sep 26, 2011 #3
    Thank you very much. I need more practice and hopefully I will get better at seeing where a formula can be differentiated to get you close.
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