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Math Help - summation algebra questions

  1. #1
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    summation algebra questions

    Find the sum of each of the following series .

    (1) \sum^{2n}_{r=n}r(2r+3)

    (2) \sum^{3n}_{r=1}r(r^2+1)
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  2. #2
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    \sum^n_{r=1} {r^2} = \frac{n(n+1)(2n+1)}{6}

     <br />
\sum^n_{r=1} {r^3} = \frac{n^2(n+1)^2}{4}<br />

     <br />
\sum^n_{r=1} {r} =\frac{n(n+1)}{2}<br />

    Use it in your case
    Last edited by mr fantastic; February 9th 2009 at 02:36 AM. Reason: Corrected first formula ..... replaced r with n on the right hand side.
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  3. #3
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    Quote Originally Posted by thereddevils View Post
    Find the sum of each of the following series .

    (1) \sum^{2n}_{r=n}r(2r+3)

    (2) \sum^{3n}_{r=1}r(r^2+1)
    Adding to what ADARSH said:

    For (1), note that

    1. \sum^{2n}_{r=n}r(2r+3) = \sum^{2n}_{r=1}r(2r+3) - \sum^{n-1}_{r=1}r(2r+3) .

    2. r(2r + 3) = 2r^2 + 3r (you should also expand the summand in (2) as well).
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