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Math Help - What does it mean to "sum a series"?

  1. #1
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    What does it mean to "sum a series"?

    The series is: \sum (-\pi ^2)^n/(2n)!9^n

    and the instruction are to "sum the series." What is expected of me here? I am supposed to make an estimation? Treat it as an alternating series? I'm not sure where to start
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  2. #2
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    Quote Originally Posted by Mattpd View Post
    The series is: \sum (-\pi ^2)^n/(2n)!9^n

    and the instruction are to "sum the series." What is expected of me here? I am supposed to make an estimation? Treat it as an alternating series? I'm not sure where to start
    what function does this series represent ?

    \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}
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    Quote Originally Posted by skeeter View Post
    what function does this series represent ?

    \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!}
    it looks to be cos(x)
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  4. #4
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    Quote Originally Posted by Mattpd View Post
    it looks to be cos(x)
    correct ... so, what is the sum of that series?
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  5. #5
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    Quote Originally Posted by skeeter View Post
    correct ... so, what is the sum of that series?
    Not sure. I take it I should have it memorized? Or solve it by approximation like other alternating series?
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    Quote Originally Posted by Mattpd View Post
    Not sure. I take it I should have it memorized? Or solve it by approximation like other alternating series?
    you just said that \sum_{n = 0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} = \cos{x} , right?

    LOOK at the your series again ... what is "x" in that series?

    \sum_{n = 0}^{\infty} \frac{(-1)^n \textcolor{red}{\pi}^{2n}}{(2n)! \cdot \textcolor{red}{3}^{2n}}
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    Pi/3?
    Last edited by Mattpd; April 29th 2010 at 06:02 PM.
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  8. #8
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    Quote Originally Posted by Mattpd View Post
    Pi/3?
    this was strictly a "recognition" problem for an infinite series representation of \cos{x} at a specific value of x ...

    \cos\left(\frac{\pi}{3}\right) = the sum of the series
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  9. #9
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    Thank you millions! So the sum of the cos function is x, and this function is the same as the cos function except with a different x value?
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    Quote Originally Posted by Mattpd View Post
    Thank you millions! So the sum of the cos function is x, and this function is the same as the cos function except with a different x value?
    This makes no sense at all! "cos function" is not a sum and so there is no "sum of a cos function". And x is the argument of the function, not the "sum".
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