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Math Help - Basic Summation

  1. #1
    Senior Member I-Think's Avatar
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    Basic Summation

    Find S_N where
    S_N= \sum_{n=N}^{N^2}(\frac{1}{n(n+1)}

    and determine
    S_N when
    \lim_{N \to infinity}

    I already got
    \sum_{n=N}^{N^2}\frac{1}{n(n+1)}=\frac{1}{N}-\frac{1}{N^2+1}
    using the method of differences but how do I use the limit to find its value at infinity?
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  2. #2
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    Add the two rational expressions to get quad/cubic and go from there.
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  3. #3
    Senior Member I-Think's Avatar
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    Your answer confuses me. Which 2 rational expressions \frac{1}{N} and \frac{1}{N^2+1}, that gives me,

    \frac{N^2+1-N}{N(N^2+1}

    which still doesen't help me.
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