My Math Forum Pi formula

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 February 17th, 2010, 04:58 AM #11 Newbie   Joined: Dec 2009 Posts: 15 Thanks: 0 Re: Pi formula Um, yeah, I'm trying to speed up the Leibniz formula for pi 8 times, however, I've run into a little problem here. I'm adding like terms of this series, and finding formulae for it. YES, it does to pi, you can even check it. n = 0 16(16(2n+1)^2 + 3)/4096n^4 + 8192n^3 + 5504n^2 + 1408n + 105 Which equates to: 304/105 + 2352/19305 + 6448/156009 + ... = Pi So yeah, I need some help here, LOL. And plus, nobody on the newsgroups would really help me. Oh, and by the way, can you guys please teach me how to get these formulae step by step?
 February 23rd, 2010, 08:30 PM #12 Global Moderator   Joined: Dec 2006 Posts: 20,305 Thanks: 1976 What problem? I posted on December 17 a method of obtaining the formula by adding fractions.
 February 25th, 2010, 01:49 PM #13 Newbie   Joined: Dec 2009 Posts: 15 Thanks: 0 Re: Pi formula I tried adding 2 terms of the formula, but it won't work!
 March 2nd, 2010, 04:19 PM #14 Global Moderator   Joined: Dec 2006 Posts: 20,305 Thanks: 1976 If you post what you did, I'll check it for you.
 March 4th, 2010, 05:05 PM #15 Newbie   Joined: Dec 2009 Posts: 15 Thanks: 0 Re: Pi formula 2(1024n^2 + 1024n + 304/4096n^4 + 8192n^3 + 5504n^2 + 1408n + 105) = 2048n^2 + 2048n + 608/4096n^4 + 8192n^3 + 5504n^2 + 1408n + 105 I just added fractions. But instead, I got twice pi!
 March 4th, 2010, 09:54 PM #16 Global Moderator   Joined: Dec 2006 Posts: 20,305 Thanks: 1976 You've multiplied by 2, so you're getting twice pi.
 March 6th, 2010, 10:22 AM #17 Newbie   Joined: Dec 2009 Posts: 15 Thanks: 0 Re: Pi formula But, it's the same denominator! Except n changes between terms, so do I treat them like different denominators?
 March 6th, 2010, 11:29 AM #18 Global Moderator   Joined: Dec 2006 Posts: 20,305 Thanks: 1976 You added the fractions correctly, using as common denominator the product of the denominators of the fractions you were adding; there was no reason to then double the numerator (which is what you did).
 March 6th, 2010, 06:08 PM #19 Newbie   Joined: Dec 2009 Posts: 15 Thanks: 0 Re: Pi formula ((1024n^2 + 1024n + 304)(4096n^4 + 8192n^3 + 5504n^2 + 1408n + 105) + (1024n^2 + 1024n + 304)(4096n^4 + 8192n^3 + 5504n^2 + 1408n + 105))/((4096n^4 + 8192n^3 + 5504n^2 + 105)(4096n^4 + 8192n^3 + 5504n^2 + 105)) Is this correct?
 March 20th, 2010, 08:13 PM #20 Global Moderator   Joined: Dec 2006 Posts: 20,305 Thanks: 1976 Why are you still effectively writing the same thing twice for no reason?

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