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Math Help - Series

  1. #1
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    Series

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

    How would I go about working this out? Any help appreciated. Thanks in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Air View Post
    \displaystyle\sum_{r=1}^{n}(\frac{1}{r} - \frac{1}{r+1})

    How would I go about working this out? Any help appreciated. Thanks in advance.
    \displaystyle\sum_{r=1}^{n}(\frac{1}{r} - \frac{1}{r+1})

    This is a telescoping sum and so equal to:

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

    (Google for telescoping sum or series to get a detailed explanation.)

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    \displaystyle\sum_{r=1}^{n}(\frac{1}{r} - \frac{1}{r+1})

    This is a telescoping sum and so equal to:

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

    (Google for telescoping sum or series to get a detailed explanation.)

    RonL

    Is that the same as method of differences? If not, how can method of differences be used?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Air View Post
    Is that the same as method of differences? If not, how can method of differences be used?

    According to Wikipedia the answer is yes.

    RonL
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