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Summation of n^2k. k = 1 to infinity

  1. Oct 5, 2005 #1
    Is the summation of k = 1 to infinity for n2k equal to
    n2 / (1 - n2)?
     
  2. jcsd
  3. Oct 5, 2005 #2
    Yes it is (for 0<=n<1).

    Alex
     
  4. Oct 5, 2005 #3
    Thanks for the confirmation.
     
  5. Oct 6, 2005 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Indeed, that is just a geometric sequence with common ratio n2.

    (I will confess that my first thought was that n must mean a positive integer, for which, of course, this does not converge!)
     
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