Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to prove this equality

  1. Apr 13, 2010 #1

    How to prove this equality:

    [tex]N\,\overline{\gamma}\sum_{k=0}^{N-1}(-1)^k\frac{{N-1\choose k}}{(k+1)^2}=\,\overline{\gamma}\sum_{k=1}^N\frac{1}{k}[/tex]?

    Thanks in advance
  2. jcsd
  3. Apr 13, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Re: Proof

    It should be relatively easy to prove it by induction.
  4. Apr 14, 2010 #3
    Re: Proof

    The result in the left hand side is my evaluation to an integral using the table of integrals and binomial expansion, and the result in the right hand side obtained from the authors, but I don't know how they did obtain it. The two results are equal and it is easy to proof that by substituting several values of N, but I am wondering if we can go from the LHS equation to the RHS systematically.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook