Express-1-2-in-terms-of-infinite-series-

Question Number 117365 by Dwaipayan Shikari last updated on 11/Oct/20

E x p r e s s (\frac{1}{2})! i n t e r m s o f i n f i n i t e s e r i e s

Commented by Dwaipayan Shikari last updated on 11/Oct/20

(\frac{1}{2})! = \frac{\sqrt{π}}{2}

1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \dots = \frac{π}{4}

\sqrt{1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \dots .} = \frac{\sqrt{π}}{2}

Answered by mindispower last updated on 11/Oct/20

(\frac{1}{2}) = \sqrt{π} = \sqrt{π} . \sum_{k ⩾ 1} \frac{1}{2^{k}}