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Math Help - Calculating Pi using Series

  1. #1
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    Calculating Pi using Series

    I am using the formula found here: http://upload.wikimedia.org/math/0/8...67293fb6b0.png

    I brake the fractions into 4 parts. A, B, C, D. A is the upper left, B is the upper right, C is the bottom left, and D is the bottom right.
    After A, B, and D are calculated by sending a number k=0 through the series (not C, because it is what represents Pi) I proceed to cross multiply to solve for C. I get A*D = B*C
    I divide by B, so really, C = AD/B
    The output is 3.14159265358973420766845359157829834076 (accurate to 13 digits after the decimal place).
    If I go through the series again and repeat the cross multiplication for the next number, k=1, then the output is -167194165969664.18081570948421477548969

    Now, at this point, should I be multiplying my values of C from previous itterations? Or should I be adding them? Or is something wrong with my calculation. Thank you for the advice!
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  2. #2
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    Quote Originally Posted by blkhockeypro19 View Post
    I am using the formula found here: http://upload.wikimedia.org/math/0/8...67293fb6b0.png

    I brake the fractions into 4 parts. A, B, C, D. A is the upper left, B is the upper right, C is the bottom left, and D is the bottom right.
    I take it you mean that A= 462880\sqrt{10005}, B= (6k)!)(13591409+ 545140134k), C= \pi, and D= (3k)!(k!)^3(-640320)^k.

    After A, B, and D are calculated by sending a number k=0 through the series (not C, because it is what represents Pi) I proceed to cross multiply to solve for C. I get A*D = B*C
    I divide by B, so really, C = AD/B
    The output is 3.14159265358973420766845359157829834076… (accurate to 13 digits after the decimal place).
    If I go through the series again and repeat the cross multiplication for the next number, k=1, then the output is -167194165969664.18081570948421477548969…
    Did you forget to do the sum? Take what you got for k=0 (before "cross multiplying") and add it to the result for k= 1. THEN "cross multiply" to find the next approximation to \pi.

    Now, at this point, should I be multiplying my values of C from previous itterations? Or should I be adding them? Or is something wrong with my calculation. Thank you for the advice!
    That " \Sigma" is a standard symbol for "sum". But you add before "cross multiplying" to get C.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    I take it you mean that A= 462880\sqrt{10005}, B= (6k)!)(13591409+ 545140134k), C= \pi, and D= (3k)!(k!)^3(-640320)^k.


    Did you forget to do the sum? Take what you got for k=0 (before "cross multiplying") and add it to the result for k= 1. THEN "cross multiply" to find the next approximation to \pi.


    That " \Sigma" is a standard symbol for "sum". But you add before "cross multiplying" to get C.
    Thanks for the reply! It helped, but for some reason, this algorithm is giving me like...100 digits per 1000 iterations. It should be faster than this. Any idea why?
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