Oblicz granicę ciągu: [latex] lim_{n o infty} (1- frac{1}{ n^{2} } )^{n} lim_{n o infty} (1- frac{3}{n} )^{n} [/latex]

[latex]displaystyle oxed{lim_{n o infty}left(1+dfrac{1}{n} ight)^n=e}[/latex] ========================== [latex]displaystyle lim_{n o infty}left(1-dfrac{1}{n^2} ight)^n=\\ lim_{n o infty}left(left(1+left(-dfrac{1}{n^2} ight) ight)^{-n^2} ight)^{- frac{1}{n}}=\\ lim_{n o infty}e^{- frac{1}{n}}=\\ 1[/latex] --------------------------------------------- [latex]displaystyle lim_{n o infty}left(1-dfrac{3}{n} ight)^n=\\ lim_{n o infty}left(left(1+left(-dfrac{3}{n} ight) ight)^{- frac{n}{3}} ight)^{-3}=\\ e^{-3}=\\ dfrac{1}{e^3}[/latex]