1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    [tex]\int_{0}^{\infty}\frac{x^3}{e^x-1}dx=\frac{\pi^4}{15}[/tex]

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

    [tex]\sum_{n=-1}^{\infty}\frac{6}{n^4}[/tex]

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

    [tex]\sum_{n=-1}^{\infty}\frac{1}{n^4}=\sum_{k=1}^{\infty}\frac{1}{k^4}[/tex]

    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

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

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




Similar Discussions: Are these two series equal?
Loading...