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Homework Help: Are these two series equal?

  1. Sep 23, 2009 #1
    Are these two series equal? (Solved)

    Not a homework problem but didn't think other forums were a better place to post this.

    I'm trying to show:

    After solving the integral, and checking it a few times, I get to this series:


    I don't know if I can just say that:


    Since the RHS is equal to [itex]\pi^4 / 90[/itex]

    If I try to just pull out the first 2 terms on the LHS then I get the sum of 1+1/0, which is bad..
    Last edited: Sep 23, 2009
  2. jcsd
  3. Sep 23, 2009 #2


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    You definitely can't say those series are equal. There is no mathematically sound way of calculation you could have gotten the LHS standing on its own as part of a solution, since it includes 1/0. There must be an error in your calculations
  4. Sep 23, 2009 #3
    Wow, thanks, just looked over what my professor did to start me off on this and noticed he made a mistake in a substitution and got n=-1 as the start of the series when it should have been n=1 so the series are equal!

    Guess I should always look over everything, not just the part that I solved.
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