Granicą ciągu an=[latex] frac{(5n+1)²}{(n-1)(n+1)} [/latex] jest liczba (proszę o rozwiązania !!!) A) 5 B) 25/2 C) 25 D) 0

[latex] lim_{n o infty} frac{(5n+1)^2}{(n-1)(n+1)} = lim_{n o infty} frac{25n^2+10n+1}{n^2-1} = \ = lim_{n o infty} frac{n^2(25+ frac{10}{n}+ frac{1}{n^2}) }{n^2(1- frac{1}{n^2}) } =25[/latex]

[latex]frac{(5n+1)^2}{(n+1)(n-1)}=frac{25n^2+10n+1}{n^2-1}[/latex] [latex]lim_{n o infty}frac{25n^2+10n+1}{n^2-1}=lim_{n o infty}frac{n^2(25+frac{10}{n}+frac{1}{n^2})}{n^2(1-frac{1}{n^2})}=frac{25}{1}=25[/latex]