1. Limited time only! Sign up for a free 30min personal 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!

How to show this convergence?

  1. Apr 28, 2015 #1
    1. The problem statement, all variables and given/known data

    I need to show that [itex]\sum\limits_{n=0}^\infty \frac{sin^{4}(\frac{n\pi}{4})}{n^2} = \frac{\pi^{2}}{16}[/itex]

    2. Relevant equations

    I have this property for odd n

    [itex]\sum\limits_{n=0}^\infty \frac{1}{n^2} = \frac{\pi^{2}}{8}[/itex]

    3. The attempt at a solution

    I have no idea how to do this, any help?
  2. jcsd
  3. Apr 29, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    There are only so many values that ##\sin(\frac{n\pi}{4})## can take. How about splitting the sum up on that basis?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: How to show this convergence?
  1. Showing Convergence (Replies: 11)

  2. Showing convergence (Replies: 13)