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Math Help - Finite sum sequence--help please!

  1. #1
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    Finite sum sequence--help please!

    Given the following finite sum
    1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+....+1/(n(n+1))

    a) Find the first 5 partial sums
    b) Make a conjecture for a formula for the sum of the first n terms
    c) Use mathematical induction to prove your formula
    Last edited by mr fantastic; April 12th 2010 at 06:43 PM.
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  2. #2
    Super Member Deadstar's Avatar
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    Quote Originally Posted by sensuji View Post
    Given the following finite sum
    1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+....+1/(n(n+1))

    a) Find the first 5 partial sums
    b) Make a conjecture for a formula for the sum of the first n terms
    c) Use mathematical induction to prove your formula
    a) You can do.

    b) \sum_{j=1}^n \frac{1}{j(j+1)} = 1 - \frac{1}{n+1}

    c) Do you know what induction is?

    Prove base case. I.e. show for n=1,

    Assume true for n.

    Prove for n+1. Hint, \sum_{j=1}^{n+1} \frac{1}{j(j+1)} = \sum_{j=1}^n \frac{1}{j(j+1)} + \frac{1}{(n+1)(n+2)}
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  3. #3
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    isn't there a prove that n=k step or something like that?
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by sensuji View Post
    isn't there a prove that n=k step or something like that?
    No you assume its true for n=k then prove it for n=k+1.

    http://en.wikipedia.org/wiki/Mathematical_induction
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