prove that ∫_0 ^∞ e^(−x^2 ) =lim_(n→+∞) ∫_0 ^∞ (dx/((1+x^2 )^n )) . 2) prove that (1/(√π)) =lim_(n→∞) ((1.3.5....(2n−3))/(2.4.6....(2n−2))) (√n) (wallis formula).


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Question Number 31106 by abdo imad last updated on 02/Mar/18

$p r o v e t h a t \int_{0}^{\infty} e^{- x^{2}} = {l i m}_{n \to + \infty} \int_{0}^{\infty} \frac{d x}{{(1 + x^{2})}^{n}} .$ $2) p r o v e t h a t \frac{1}{\sqrt{π}} = {l i m}_{n \to \infty} \frac{1.3.5 . . . . (2 n - 3)}{2.4.6 . . . . (2 n - 2)} \sqrt{n}$ $(w a l l i s f o r m u l a) .$
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