Estimate Pi as described in the following link: http://www.people.virginia.edu/~teh1m/cody/Pi_estimation2.pdf
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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
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.
The error noted above has been corrected.
The pdf file link is broken.
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.
Thanks Rafael!
For the record the stopping condition should use 10^-d, not 10^-n.
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.