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Math Help - Summation question

  1. #1
    Senior Member
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    Summation question

    \sum\limits_{k = 0}^{n} \frac{2(k + 1)}{(n + 1)(n + 2)}

    How do I solve this? My brain is failing me.

    Any advice would be great.
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  2. #2
    A Plied Mathematician
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    Everything in the summand that does not contain a k can be factored out of the summand. What does that do for you?
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  3. #3
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    \frac{2}{(n + 1)(n + 2)}\sum\limits_{k = 0}^{n} (k + 1)

    So the summation becomes:

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


    My brain is still stuck. 40C/104F+ temps are killing me. >_<
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  4. #4
    MHF Contributor
    skeeter's Avatar
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    maybe you remember this ...

    1+2+3+...+n = \dfrac{n(n+1)}{2}
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  5. #5
    A Plied Mathematician
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    Also,

    \displaystyle\sum_{k=1}^{n}1=n.
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  6. #6
    Math Engineering Student
    Krizalid's Avatar
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    wonder if the sum is full of typos or if the problem tries to bust you.
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