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Thread: evaluating pi and e from integer series like golden ratio

  1. #1
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    evaluating pi and e from integer series like golden ratio

    Apologies if I'm in the wrong forum.

    The ratio of two successive terms in the Fibonacci series converges on the golden ratio. Are there equivalent number series that evaluate pi or e?
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  2. #2
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    \displaystyle \pi = 4\sum_{i=0}^{\infty}\frac{(-1)^i}{2i+1}

    Make x=1 in this case

    \displaystyle e^x = \sum_{i=0}^{\infty}\frac{x^i}{i!}
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  3. #3
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    EDIT: way too slow!

    Quote Originally Posted by interestingdave View Post
    Are there equivalent number series that evaluate pi or e?
    I'm not sure if it's what you want, but the sum of alternating series of reciprocals of odd numbers is \frac{\pi}{4}.
    Also, one of the definition of e is the sum of the series of reciprocal factorial numbers. See here, btw.
    Last edited by TheCoffeeMachine; Feb 3rd 2011 at 12:57 PM.
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