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Math Help - Finding a formula

  1. #1
    Junior Member mremwo's Avatar
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    Finding a formula

    1. Find a formula for
    1/(1x2) + 1/(2x3)+...+ 1/n(n+1) by examining values for small values of n.

    2. prove the formula

    -why am I being asked to find a formula? is the summation of all values of n up to i (the formula given) not sufficient?

    thanks
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  2. #2
    MHF Contributor chisigma's Avatar
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    Is...

    \displaystyle \frac{1}{n\ (n+1)} = \frac{1}{n} - \frac{1}{n+1} (1)

    ... so that...

    \displaystyle \frac{1}{1 \cdot 2} +  \frac{1}{2 \cdot 3} + \dots +  \frac{1}{n \cdot (n+1)} = 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \dots + \frac{1}{n} - \frac{1}{n+1} = 1 -\frac{1}{n+1} (2)

    Kind regards

    \chi \sigma
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  3. #3
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    Quote Originally Posted by mremwo View Post
    1. Find a formula for
    1/(1x2) + 1/(2x3)+...+ 1/n(n+1) by examining values for small values of n.

    2. prove the formula

    -why am I being asked to find a formula? is the summation of all values of n up to i (the formula given) not sufficient?

    thanks

    Hint: \frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}

    Tonio
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