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Math Help - Sum of Quadratic Series!

  1. #1
    Senior Member sakonpure6's Avatar
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    Sum of Quadratic Series!

    I have the quadratic n^2 with 17 terms. So, the series is 1 + 4 + 9 +16 + 25+......+289

    How do I find the sum of this series other than punching in the numbers in my calculator? any help is appreciated
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    Re: Sum of Quadratic Series!

    Quote Originally Posted by sakonpure6 View Post
    I have the quadratic n^2 with 17 terms. So, the series is 1 + 4 + 9 +16 + 25+......+289
    Surely you know about the special sums?

    \sum\limits_{k = 1}^N {k^2 }  = \frac{{N(N + 1)(2N + 1)}}{6}
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    Senior Member sakonpure6's Avatar
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    Re: Sum of Quadratic Series!

    lol no, this is a bonus question and your equation does work.. I saw a simpler one on yahoo answer with the same right side of the equation but with out the left... Do you know how we can conclude this equation from several calculations?

    and, how about if we a have a cubic power series?

    Edit: I found out the equation for the cubic power series and is as follows, Sum = ((n(n+1))/2)^2
    Last edited by sakonpure6; January 7th 2013 at 03:36 PM.
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    Re: Sum of Quadratic Series!

    Quote Originally Posted by sakonpure6 View Post
    and, how about if we a have a cubic power series?
    You could have found this webpage for yourself.
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