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Math Help - Sum of known series.?

  1. #1
    Member zangestu888's Avatar
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    Sum of known series.?

    Find the sum of the series:

    Infinte series from n=0 to infinte (-1)^n * (pi^2n+1)/(4^2n+1)(2n+1)!

    i know the sin series looks like that becuase sin is

    (-1)^n*x^2n+1/(2n+1)! but i dont get the 4 part in the expression, the answer is sin pi/4=1/sqrt2 but how? steps will be helpful please. thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zangestu888 View Post
    Find the sum of the series:

    Infinte series from n=0 to infinte (-1)^n * (pi^2n+1)/(4^2n+1)(2n+1)!

    i know the sin series looks like that becuase sin is

    (-1)^n*x^2n+1/(2n+1)! but i dont get the 4 part in the expression, the answer is sin pi/4=1/sqrt2 but how? steps will be helpful please. thanks!
    \sin x = \sum_{n = 0}^\infty (-1)^n \frac {x^{2n + 1}}{(2n + 1)!}

    replace x with \frac {\pi}4, what do you get?
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