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Math Help - sum fof series?

  1. #1
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    sum fof series?

    How do we find the sum of the below series:
    a)
    1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
    b)
    1/2 + 1/6 + 1/12 + 1/20 + ......

    Thanks!!!
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  2. #2
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    Quote Originally Posted by a69356 View Post
    How do we find the sum of the below series:
    a)
    1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
    b)
    1/2 + 1/6 + 1/12 + 1/20 + ......

    Thanks!!!
    (b) \sum_{n=1}^{\infty} \frac{1}{n(n+1)} = \sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1} =

    \left(1 - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + ... + \left(\frac{1}{n-1} - \frac{1}{n}\right) + \left(\frac{1}{n} - \frac{1}{n+1}\right) + ... =

    \lim_{n \to \infty} 1 - \frac{1}{n+1} = 1


    the series in (a) is just twice the sum of (b).
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