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Thread: How to simplify this sum

  1. #1
    Junior Member
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    How to simplify this sum

    $$\frac{k^2(k+1)^2}{4} + (k+1)^3$$


    I am trying to simplify it down to

    $$[\sum_{i=1}^{k+1} i]^2$$

    Think I figured it out

    $$(k+1)^2(\frac{k^2}{4} + (k+1)) = \frac{(k+1)^2(k^2+4k+4)}{4} = \frac{(k+1)^2(k+2)^2}{4} = [\frac{(k+1)(k+2)}{2}]^2 = [\sum_{i=1}^{k+1} i]^2]$$
    Last edited by mdm508; Jan 10th 2018 at 12:30 AM. Reason: Need verification of correctness
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  2. #2
    MHF Contributor
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    Re: How to simplify this sum

    That's correct
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