Happy Pi day
Posted: Wed Mar 14, 2012 6:12 pm
Happy Pi day to everyone.Wish a loong and meaningful life to everyone.I'll ask everyone to post any wonderful fact about pi here.I'm starting by giving a self-made series of computing value of $\pi$.
\[ \pi = \frac{102857 - 4480 \sqrt{108}}{17920} - 3 \sum_{n = 2}^{\infty}
\left( \frac{\prod_{k = n}^{2 n - 1} \left( 2 k + 1 \right)}{2^{7 n - 1}
n!} \left( \frac{1}{4 n + 1} + \frac{4 n + 1}{4 \left( 4 n + 2 \right)
\left( 4 n + 3 \right)} \right) \right) \]
\[ \pi = \frac{102857 - 4480 \sqrt{108}}{17920} - 3 \sum_{n = 2}^{\infty}
\left( \frac{\prod_{k = n}^{2 n - 1} \left( 2 k + 1 \right)}{2^{7 n - 1}
n!} \left( \frac{1}{4 n + 1} + \frac{4 n + 1}{4 \left( 4 n + 2 \right)
\left( 4 n + 3 \right)} \right) \right) \]