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Question Number 8277 by Yozzias last updated on 05/Oct/16

Show that one representation for π \approx 3.14 \dots

is π = {12 \cos}^{- 1} [{(\frac{3}{4})}^{1 / 4} (1 + \underset{r = 1}{\sum^{\infty}} \frac{\underset{k = 1}{\prod^{2 r}} (\frac{3}{2} - k)}{(2 r)!} {(\frac{- 1}{3})}^{r})] .