Results 1 to 3 of 3

Math Help - Mathematical Induction question

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    2

    Mathematical Induction question

    Hey there guys i was wondering if someone would be able to help me out. I have to get this done by tomorrow at 4:00PM so the faster the better. Here is the problem,
    by mathermatical induction prove

    n Sigma i=1 1/(2i-1)(2i+1) = n/2n+1

    As you know the n is on top of the sigma and the i=1 at the bottom of the sigma

    Thank you kn advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Evil Colt View Post
    Hey there guys i was wondering if someone would be able to help me out. I have to get this done by tomorrow at 4:00PM so the faster the better. Here is the problem,
    by mathermatical induction prove

    n Sigma i=1 1/(2i-1)(2i+1) = n/2n+1

    As you know the n is on top of the sigma and the i=1 at the bottom of the sigma

    Thank you kn advance
    I assume you can do the first two steps. Then the trouble is in step 3, showing that the result is true for n + 1 assuming it's true for n.

    So it boils down to showing that \frac{n}{2n+1} + \frac{1}{(2[n+1] - 1)(2[n+2] + 1)} = \frac{n+1}{2(n+1) + 1}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517
    I think you can verify the base case for n=1.

    So you assume the equality holds up to k. You must show it holds for k+1 for the induction to be complete.

    \sum_{i=1}^{k+1}\frac{1}{(2i-1)(2i+1)}=\sum_{i=1}^{k}\frac{1}{(2i-1)(2i+1)}+\frac{1}{(2(k+1)-1)(2(k+1)+1)}
    =\frac{k}{2k+1}+\frac{1}{(2k+1)(2k+3)}=\frac{k(2k+  3)+1}{(2k+1)(2k+3)}=\frac{(2k+1)(k+1)}{(2k+1)(2k+3  )}=\frac{(k+1)}{(2k+3)}<br />
=\frac{(k+1)}{2(k+1)+1}

    this completes the induction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Mathematical Induction Question
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: March 29th 2010, 12:31 PM
  2. Need help on Mathematical Induction question
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 27th 2008, 11:32 AM
  3. Mathematical Induction Question
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: June 24th 2008, 06:11 AM
  4. Mathematical Induction Question
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 23rd 2008, 11:40 PM
  5. yet another Mathematical Induction question
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: June 21st 2007, 08:15 PM

Search Tags


/mathhelpforum @mathhelpforum