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Math Help - Mathematical Induction

  1. #1
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    Exclamation Mathematical Induction

    Use mathematical induction to prove that


    n
    Σ 2/r(r^2-1) = (1/2) - (1/n(n+1)) n= 2,3,4.......
    r=2

    i have done the basic proof and got to the point


    k+1
    Σ = (1/2) - (1/k(k+1)) + 2/(k+1)(k+1^2-1)
    r=2


    I think i need to get to (1/2) - 1/(k+1)(k+2) but im not sure how to get there, any help would be greatly appreciated!
    Last edited by gurnster76; May 23rd 2012 at 07:05 AM.
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  2. #2
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    Re: Mathematical Induction

    Quote Originally Posted by gurnster76 View Post
    Use mathematical induction to prove that
    n
    Σ 2/r(r^2-1) = (1/2) - (1/n(n+1)) n= 2,3,4.......
    r=2

    i have done the basic proof and got to the point

    k+1
    Σ = (1/2) - (1/k(k+1)) + 2/(k+1)(k+1^2-1)
    r=2
    Work with
    \frac{1}{2}-\frac{1}{k(k+1)}+\frac{2}{(k+1)((k+1)^2-1)}=~?
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  3. #3
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    Re: Mathematical Induction

    That's where im stuck.
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  4. #4
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    Re: Mathematical Induction

    Quote Originally Posted by gurnster76 View Post
    That's where im stuck.
    \frac{2}{(k+1)((k+1)^2-1)}=\frac{2}{(k+1)(k^2+2k)}=\frac{2}{k(k+1)(k+2)}
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  5. #5
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    Re: Mathematical Induction

    but how do i get from

    (1/2) - (1/k(k+1)) + (2/(k+1)(k+2)

    to (1/2) - (1/(k+1)(k+2)
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