Znajdź granicę ciągu o wyrazie ogólnym Un = (1-4/n)^(-n+3)

[latex] lim_{n o infty} (1-4/n)^{(-n+3)}[/latex]= =[latex] lim_{n o infty} (1-4/n)^{(-n/4)*(-4/n)*(-n+3)}[/latex]= [latex]lim_{n o infty} e^{(-4/n)*(-n+3)} [/latex]} = =[latex] lim_{n o infty} ( e^{4} + e^{ frac{-12}{n}}) = e^{4} [/latex]

[latex]limlimits_{n oinfty} left(1-dfrac{4}{n} ight)^{-n+3}=limlimits_{n oinfty} left(1+dfrac{4}{-n} ight)^{-n+3}= \ \ \ = limlimits_{n oinfty} left( left( left( 1+dfrac{4}{-n} ight)^{frac{-n}{4}} ight)^{frac{4}{-n}} ight)^{-n+3}=limlimits_{n oinfty} e^{frac{4(-n+3)}{-n}}= \ \ \ = limlimits_{n oinfty} e^{frac{-4n+12}{-n}}= e^{frac{-4}{-1}}=e^4[/latex]