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Fraction series tending to p/2
By Chris Park on Wednesday, September 26, 2001 - 06:02 am:

What is the value of Tn (nth term) of this sequence as n goes to infinity?


 2
1
 ,  2×2
1×3
 ,  2×2×4
1×3×3
 ,  2×2×4×4
1×3×3×5
 ,  2×2×4×4×6
1×3×3×5×5
 ,  2×2×4×4×6×6
1×3×3×5×5×7


Thank you! :)
By Arun Iyer on Thursday, September 27, 2001 - 08:06 pm:

lim
n®¥ 
 æ
è		  2×2×4×4×6...(2n)(2n)
1×3×3×5×5...(2n-1)(2n-1)(2n+1)
 ö
ø		 =  p
2

This is called the Wallis formula.

love arun
By The Editor

This gives one way of calculating p.

  • Start with 2
  • Multiply by 2/1, 2/3, 4/3, 4/5, 6/5, 6/7, etc
It takes a while to converge, but it would be reasonably easy to set up a short program to do it.