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find the sum of the series?

sigma notation (( (-1)^n * pi^2n)) / (6^2n * (2n)!) as n=0 goes to ininity

4 Answers

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  • 1 decade ago
    Favorite Answer

    The maclaurin series for cos x is

    1 - x^2/2! + x^4/4! - x^6/6!....

    If we let x = pi/6 in the above expansion we recognize that your series is the series of cospi/6

    √3/2

  • 4 years ago

    Find The Sum Of Series

  • Anonymous
    1 decade ago

    It's a cos expansion evaluated at Pi/6 =>

    =cos(Pi/6)=Sqrt(3)/2

  • 1 decade ago

    (-1)^n (Pi^2n)/(6^2n*(2n)!) use ratio test

    (Pi^2(n+1)/6^2n*(2(n+1)!))*(6^2n*(2n)!)/(Pi^2n)

    Pi^2*(2n)!/(2n+2)(2n+1)(2n!)

    Pi^2/(2n+2)(2n+1)=Pi^2/INFINITY

    =0

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