Oblicz granicę ciągu an [latex] lim_{n o infty} a_n = frac{(n+2) ^{2} }{(2n-1) ^{2} } [/latex] [latex] lim_{n o infty} a_n = frac{(n ^{2} +1)(6-4n ^{2}) }{(n-1)(n ^{3}+1) } [/latex]

[latex]\lim_{n oinfty}frac{n^2+4n+4}{4n^2-4n+1}=lim_{n oinfty}frac{1+frac4n+frac{4}{n^2}}{4-frac4n+frac{1}{n^2}}=frac14 \ \lim_{n oinfty}frac{-4n^4+6n^2-4n^2+6}{n^4-n^3+n-1}= \ \lim_{n oinfty}frac{-4+frac{2}{n^2}+6/n^4}{1-frac1n+1/n^3-1/n^4}=-4[/latex]