summations

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  1. 041087's Avatar
    1 29-07-2012  06:37
    • Full Member
    • Posts: 90
    summations
    can somebody tell me why the following is true?
    Click image for larger version.  Name: f1e60f170b4ab46ad57feb2fc95fe995.png  Views: 13  Size: 1,000 Bytes  ID: 165601
    thanks
  2. notnek's Avatar
    2 29-07-2012  07:11
    • TSR Demigod
    • Location: Bangkok, Thailand
    Re: summations
    (Original post by 041087)
    can somebody tell me why the following is true?
    Click image for larger version.  Name: f1e60f170b4ab46ad57feb2fc95fe995.png  Views: 13  Size: 1,000 Bytes  ID: 165601
    thanks
    Are you trying to prove it?


    You can use:

    \displaystyle \sum_{i \mathop = 0}^n i = \frac {n \left({n + 1}\right)} 2

    and then prove the following by induction:

    \displaystyle \sum_{i \mathop = 0}^n i^3 = \frac{n^2 \left({n + 1}\right)^2} 4
  3. 041087's Avatar
    3 29-07-2012  08:47
    • Full Member
    • Posts: 90
    Re: summations
    (Original post by notnek)
    Are you trying to prove it?


    You can use:

    \displaystyle \sum_{i \mathop = 0}^n i = \frac {n \left({n + 1}\right)} 2

    and then prove the following by induction:

    \displaystyle \sum_{i \mathop = 0}^n i^3 = \frac{n^2 \left({n + 1}\right)^2} 4
    thanks
    it is more easier for me to remember the formula after i know how to prove it
    Last edited by 041087; 29-07-2012 at 08:51.
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