Results 1 to 4 of 4

Math Help - find the sum of the series question **

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    158

    find the sum of the series question **

    find the sum of 1/[n(n+3)]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    S= \sum_{n=1}^{\infty} \frac{1}{n\cdot (n+3)} = \frac{1}{3}\cdot \sum_{n=1}^{\infty} (\frac{1}{n} - \frac{1}{n+3}) =

     =\frac{1}{3}\cdot  (1 + \frac{1}{2} + \frac{1}{3} +\frac{1}{4} - \frac{1}{4} + \frac{1}{5} - \frac{1}{5} + \dots) = \frac{1}{3}\cdot \frac{11}{6} = \frac{11}{18}

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2008
    Posts
    158
    why multiply by 11/6?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    The term \frac{11}{6} derives from...

    1 + \frac{1}{2} + \frac{1}{3} = \frac{11}{6}

    In general is...

    \sum_{n=1}^{\infty} \frac{1}{n\cdot (n+k)} = \frac{1}{k} \cdot \sum_{i=1}^{k} \frac{1}{i}

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: September 29th 2010, 07:11 AM
  2. Replies: 0
    Last Post: January 26th 2010, 09:06 AM
  3. Binomial Series to find a Maclaurin Series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 21st 2009, 08:15 AM
  4. find the sum of a series q
    Posted in the Calculus Forum
    Replies: 6
    Last Post: May 15th 2009, 07:36 AM
  5. Sequences and Series - Power Series Question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2008, 08:32 PM

Search Tags


/mathhelpforum @mathhelpforum