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

Express ((1/2))!  in terms of infinite series

Express(12)!intermsofinfiniteseries

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

((1/2))!=((√π)/2)  1−(1/3)+(1/5)−(1/7)+(1/9)−...=(π/4)  (√(1−(1/3)+(1/5)−(1/7)+(1/9)−....))=((√π)/2)

(12)!=π2113+1517+19...=π4113+1517+19....=π2

Answered by mindispower last updated on 11/Oct/20

((1/2))=(√π)=(√π).Σ_(k≥1) (1/2^k )

(12)=π=π.k112k

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