Problem 954. Pi Estimate 2

Created by Ed Hall

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Estimate Pi as described in the following link: http://www.people.virginia.edu/~teh1m/cody/Pi_estimation2.pdf

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Last Solution submitted on Jan 08, 2026

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Richard Zapor on 23 Sep 2012

I do not feel the solution set matches the Challenge definition. The solution appears to use the delta from Pi instead of the defined estimate differential delta.
The correct answers are:
9 3.1415917732 delta=4.16658e-7
6 3.1415266183 delta=3.2042972e-5
12 3.1415926414 delta=5.693e-9

Richard Zapor on 24 Sep 2012

Appears the expected solution can be achieved if use T(n+1)-Tn instead of the problem definition of t(n+1)-tn. The scale factor makes a significant difference.

Ed Hall on 16 Oct 2012

The error noted above has been corrected.

Rafael S.T. Vieira on 28 Aug 2020

The pdf file link is broken.

Rafael S.T. Vieira on 27 Sep 2020

It seems that the formula is an infinite sum of factorial(n)^2/factorial(2*n+1) (starting at zero) multiplied by
9/(2*sqrt(3)), When (current sum - previous sum) < 10^-n then we should stop the infinite sum. One expected output is the number of summands and the other is our estimated value for pi (rounded to 10 decimal places) in this order. Good luck for anyone trying.

Christian Schröder on 24 Oct 2022

Thanks Rafael!

For the record the stopping condition should use 10^-d, not 10^-n.

minnolina on 1 Jun 2024

More precisely, we aim to utilize the relation
$$ \sum_{n=1}^{\infty} \frac{(n!)^2}{(2n+1)!} = \frac{2\sqrt{3}}{9}\pi-1 $$
to estimate the value of $\pi$ by iteratively adding terms from this series and comparing successive partial sums to a desired level of accuracy.

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Problem 954. Pi Estimate 2

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Problem 954. Pi Estimate 2

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