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Math Help - Series

  1. #1
    Junior Member
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    Series

    Hi guys, got a question which I need help in:

    Show that the kth term of the series
    1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) +... is 2[1/k - 1/(1+k)]
    Hence find the sum of the first 50 terms.

    I haven't done this type of question before so I really don't know how to start... Doesn't seem like I can apply arithmetric/geometric progression to solve too...

    Thanks in advance!
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Blizzardy View Post
    Hi guys, got a question which I need help in:

    Show that the kth term of the series
    1 + 1/(1+2) + 1/(1+2+3) + 1/(1+2+3+4) +... is 2[1/k - 1/(1+k)]
    Hence find the sum of the first 50 terms.

    I haven't done this type of question before so I really don't know how to start... Doesn't seem like I can apply arithmetric/geometric progression to solve too...

    Thanks in advance!
    Hint the denominators are the sum of the first n integers

    1+2+3+4+...n=\frac{n(n+1)}{2}

    Can you use this to rewrite the series? It wont be geometric or arithmetic but try partial fractions.
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