Results 1 to 2 of 2

Math Help - Induction

  1. #1
    Newbie
    Joined
    Sep 2008
    From
    Stockholm
    Posts
    15

    Induction

    Hi there!
    This is my problem
    Calculate \sum_{k=1}^n \frac{1}{(2k-1)(2k+1)} And then prove it, with help of induction?

    Can any one of you help me with this problem?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Kluringen View Post
    Hi there!
    This is my problem
    Calculate \sum_{k=1}^n \frac{1}{(2k-1)(2k+1)} And then prove it, with help of induction?

    Can any one of you help me with this problem?
    if you get to the expression it should be equal to, can you do the induction?

    this is a telescoping sum. meaning, you can write it in a different form that when you expand it, most of the terms will cancel out, leaving you with what the sum actually is.

    note that \frac 1{(2k - 1)(2k + 1)} = \frac 12 \bigg( \frac 1{2k - 1} - \frac 1{2k + 1} \bigg) (if you can't expand like that using algebra, just use partial fractions)

    so that \sum_{k = 1}^n \frac 1{(2k - 1)(2k + 1)} = \frac 12 \sum_{k = 1}^n \bigg( \frac 1{2k - 1} - \frac 1{2k + 1} \bigg)

    now expand the sum on the right to see what cancels out. that will get you your formula to do the induction with
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Strong induction vs. structural induction?
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: April 21st 2011, 01:36 AM
  2. Replies: 10
    Last Post: June 29th 2010, 01:10 PM
  3. induction help
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: April 19th 2010, 06:39 AM
  4. Mathemtical Induction Proof (Stuck on induction)
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 8th 2009, 10:33 PM
  5. Induction!
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 7th 2008, 05:10 PM

Search Tags


/mathhelpforum @mathhelpforum