Pi Approximation Day

[Steve Simpkin]

(07-23-2022 05:18 PM)C.Ret Wrote:  \( \sqrt{10-\frac{1}{\left ( 10^2+10 \right )^3}-\frac{1}{\left ( 9^2+9 \right )^3}-\frac{1}{\left ( 8^2+8 \right )^3}-\cdots -\frac{1}{\left ( 2^2+2 \right )^3}-\frac{1}{\left ( 1^2+1 \right )^3}} = \sqrt{ \frac{2\,780\,722\,699}{281\,746\,080} } \approx \pi \)

Interesting.
Using that equation with a summation of 1-10 approximates Pi to 7 digits.
Using it with a summation of 1-87 approximates Pi to 12 digits.