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Homework Help: 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


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    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?
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