Results 1 to 6 of 6

Math Help - Sum of series to infinite

  1. #1
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Sum of series to infinite

    \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Sum of series to infinite

    \frac{u_{n+1}}{u_n}=\ldots=\frac{n}{n+3}=\frac{ \alpha n+\beta}{\alpha n+\gamma} (hipergeometric series) . According to a well known theorem , S=\frac{u_1\gamma}{\gamma-(\alpha+\beta)}=\ldots=\frac{1}{4}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Re: Sum of series to infinite

    Quote Originally Posted by FernandoRevilla View Post
    \frac{u_{n+1}}{u_n}=\ldots=\frac{n}{n+3}=\frac{ \alpha n+\beta}{\alpha n+\gamma} (hipergeometric series) . According to a well known theorem , S=\frac{u_1\gamma}{\gamma-(\alpha+\beta)}=\ldots=\frac{1}{4}
    More detail, please?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    44

    Re: Sum of series to infinite

    Quote Originally Posted by BabyMilo View Post
    More detail, please?
    What methods have you covered, please?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Feb 2008
    Posts
    383

    Re: Sum of series to infinite

    Quote Originally Posted by FernandoRevilla View Post
    What methods have you covered, please?

    I havent been taught how to do this really.
    I have covered the test for convergent but the book asks for this.
    I used partial fraction which they all diverges.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,324
    Thanks
    8

    Re: Sum of series to infinite

    Note that

    \frac{1}{n(n+1)(n+2)} = \frac{1}{2}\left(\frac{1}{n} - \frac{1}{n+1}\right) -  \frac{1}{2}\left(\frac{1}{n+1} - \frac{1}{n+2}\right)

    Write some terms in the series

    \sum_{n=1}^{\infty} \frac{1}{2}\left(\frac{1}{n} - \frac{1}{n+1}\right) -  \frac{1}{2}\left(\frac{1}{n+1} - \frac{1}{n+2}\right)

    and see what happens.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Fourier series to calculate an infinite series
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 4th 2010, 01:49 PM
  2. Replies: 7
    Last Post: October 12th 2009, 10:10 AM
  3. Replies: 2
    Last Post: September 16th 2009, 07:56 AM
  4. infinite series and power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 13th 2009, 04:21 AM
  5. Replies: 1
    Last Post: May 5th 2008, 09:44 PM

Search Tags


/mathhelpforum @mathhelpforum