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Math Help - pi summation formula

  1. #1
    Eater of Worlds
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    pi summation formula

    Has anyone seen this one before?.

    \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right  )^{n}

    It works rather well and quick. At n=6 you get 3.14159265357
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  2. #2
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    Quote Originally Posted by galactus View Post
    Has anyone seen this one before?.

    \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right  )^{n}

    It works rather well and quick. At n=6 you get 3.14159265357
    No.

    The best one I ever seen was made by Srinivasa Ramanajuan. (search the article for his formula).
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by galactus View Post
    Has anyone seen this one before?.

    \pi=\sum_{n=0}^{\infty}\left(\frac{4}{8n+1}-\frac{2}{8n+4}-\frac{1}{8n+5}-\frac{1}{8n+6}\right)\cdot\left(\frac{1}{16}\right  )^{n}

    It works rather well and quick. At n=6 you get 3.14159265357
    Never seen that before, but that's nice! I'd love to see how it was derived
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