prove-that-0-e-x-2-lim-n-0-dx-1-x-2-n-2-prove-that-1-pi-lim-n-1-3-5-2n-3-2-4-6-2n-2-n-wallis-formula-

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 \dots . (2 n - 3)}{2.4.6 \dots . (2 n - 2)} \sqrt{n}

(w a l l i s f o r m u l a) .