Results 1 to 2 of 2

Thread: General formula of a series

  1. July 20th 2010, 07:43 PM #1
    TerenceCS
    TerenceCS is offline
    Newbie
    Joined
    Jul 2010
    Posts
    9

    Post General formula of a series

    Hi everyone! I have some problems in understanding the following general formula:
    \displaystyle S_n=\sum_{k=2}^{n} \frac{1}{k^2-1}=\frac{3}{4}-\frac{1}{2n}-\frac{1}{2(n+1)}
    Does anyone have a proof for this? Any effort will be appreciated.
    Follow Math Help Forum on Facebook and Google+
  2. July 20th 2010, 07:55 PM #2
    nehme007
    nehme007 is offline
    Junior Member
    Joined
    Nov 2009
    Posts
    69
    Replace \frac{1}{k^2-1} with its partial fraction decomposition, then write out the series term by term. A bunch of stuff should cancel leaving the desired result.
    Follow Math Help Forum on Facebook and Google+
« integral of 2y^2 / (16+y^2) dy | Finding the differential of dy »

Similar Math Help Forum Discussions

  1. General Diagonal Formula
    Posted in the Geometry Forum
    Replies: 9
    Last Post: November 14th 2011, 04:28 PM
  2. sequence general formula
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 28th 2009, 12:15 PM
  3. General Formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 20th 2009, 12:27 PM
  4. 1,1,1,1 Matrix general formula!!!
    Posted in the Advanced Algebra Forum
    Replies: 20
    Last Post: April 27th 2008, 05:23 AM
  5. general integration formula
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 20th 2008, 08:26 AM

Search Tags


/mathhelpforum @mathhelpforum