Lim(n→∞)(n-√(n^2+3)); б) lim/(n→∞) 7^n/n!

[latex] lim_{n o infty} (n- sqrt{n^2+3})= lim_{n o infty} frac{ (n- sqrt{n^2+3})cdot (n+ sqrt{n^2+3})}{(n+ sqrt{n^2+3})}= \ \ = lim_{n o infty} frac{ (n)^2- (sqrt{n^2+3})^2}{(n+ sqrt{n^2+3})}= lim_{n o infty} frac{ n^2- n^2-3}{n+ sqrt{n^2+3}}= lim_{n o infty} frac{ -3}{n+ sqrt{n^2+3}}=0 [/latex][latex] lim_{n o infty} frac{7^{n}}{n!} = lim_{n o infty} frac{7^{n}}{ sqrt{2 pi n}cdot ( frac{n}{e})^{n} } = \ \ = lim_{n o infty} frac{(7e)^{n}}{ sqrt{2 pi n}cdot (n)^{n} } = lim_{n o infty} frac{1}{ sqrt{2 pi n} } cdot (frac{7e}{n})^n =0[/latex]Формула Стирлинга n! ≈ [latex] sqrt{2 pi n} cdot ( frac{n}{e})^{n} [/latex]