Results 1 to 4 of 4

Math Help - Sums and Fourier Series 2

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    5

    Sums and Fourier Series 2

    Use the answer to the Fourier series:
    for

    Compute sum:

    [(-1)^n] / (2n+1)

    Some starting points would be greatly appreciated!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Try putting x=\pi/2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    5
    Quote Originally Posted by Opalg View Post
    Try putting x=\pi/2.
    Thank you, I've tried this. However, I still don't see where to get
    SUM 1/(2n+1)

    I think I am missing a fundamental step. Any ideas?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Chitownmegs View Post
    Thank you, I've tried this. However, I still don't see where to get
    SUM 1/(2n+1)

    I think I am missing a fundamental step. Any ideas?
    \sin\pi/2 = 1,\ \sin2\pi/2=0,\ \sin3\pi/2=-1,\ \sin4\pi/2=0,\ \sin5\pi/2=-1, and in general \sin(2m\pi/2)=0,\ \sin((2m+1)\pi/2) = (-1)^m.

    Therefore in the sum \sum_{n=1}^\infty \frac{(-1)^{n+1}}n\sin(n\pi/2), only the odd-numbered terms are nonzero. So try putting n=2m+1, with the sum going from m=1 to ∞.
    Last edited by Opalg; November 13th 2008 at 02:04 PM. Reason: Silly mistake, as so often
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: April 13th 2011, 12:39 PM
  2. [SOLVED] Question about the lower limit of sums in Fourier series
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 28th 2010, 12:40 PM
  3. Complex Fourier Series & Full Fourier Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 9th 2009, 06:39 AM
  4. Computing Sums given Fourier Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 12th 2008, 04:18 AM
  5. from fourier transform to fourier series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 1st 2008, 07:35 AM

Search Tags


/mathhelpforum @mathhelpforum