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Math Help - Finding pi as a sum of rational number :]

  1. #1
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    Exclamation Finding pi as a sum of rational number :]

    Well I'm abit curious about the Taylor Series-

    Suppose f(x)= arctan(x)

    Lets find the taylor series of f(x)....

    We get that

    arctan(x)= SUM n=0 --> infinity [x- x^3/3 + x^5/5 -x^7/7 ..... (-1)^(n+1)*x^(n+1) / (n+1) .......... ]

    lets assume that its keeps going and there is no end point k

    when we sub in x=1

    we get

    pi/4= 1-1/3+1/5+1/7 + .................+ 1/(n+2) +.........


    now multiply both by 4

    we should get pi is approx = 4 -4/3 +4/5 +4/7 ............. + 4/(n+2) +.....

    Is this enough ??

    is there a proof where it shows pi can be written in rational/irrational numbers etc..

    I know my proof seems sort of dodgy- but please correct me

    Thanks for your time and effort.
    Last edited by Khonics89; May 30th 2009 at 09:38 PM.
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  2. #2
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    you made a typo with -4/2 as it should be -4/3 but otherwise

    Leibniz formula for pi - Wikipedia, the free encyclopedia

    your proof is certainly convincing enough even if not as rigorous as it could be
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  3. #3
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    Quote Originally Posted by Khonics89 View Post
    Well I'm abit curious about the Taylor Series-

    Suppose f(x)= arctan(x)

    Lets find the taylor series of f(x)....

    We get that

    arctan(x)= SUM n=0 --> infinity [x- x^3/3 + x^5/5 -x^7/7 ..... (-1)^(n+1)*x^(n+1) / (n+1) .......... ]

    lets assume that its keeps going and there is no end point k

    when we sub in x=1

    we get

    pi/4= 1-1/3+1/5+1/7 + .................+ 1/(n+2) +.........


    now multiply both by 4

    we should get pi is approx = 4 -4/2 +4/5 +4/7 ............. + 4/(n+2) +.....

    Is this enough ??

    is there a proof where it shows pi can be written in rational/irrational numbers etc..

    I know my proof seems sort of dodgy- but please correct me

    Thanks for your time and effort.
    Pi - Wikipedia, the free encyclopedia
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  4. #4
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    ohh ok nice websites
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