Zad. Oblicz granice poniższego ciągu [latex] lim_{n o infty} frac{5}{ sqrt{ n^{2}+7n } -n} [/latex] wynik ma wyjść [latex] frac{10}{7} [/latex]

[latex]displaystyle lim_{n oinfty} dfrac{5}{sqrt{n^2+7n}-n} = lim_{n oinfty} dfrac{5}{sqrt{n^2+7n}-n} cdotdfrac{sqrt{n^2+7n}+n}{sqrt{n^2+7n}+n}=\=lim_{n oinfty} dfrac{5cdot(sqrt{n^2+7n}+n)}{n^2+7n-n^2} = lim_{n oinfty} dfrac{5cdot(sqrt{n^2+7n}+n)}{7n} = \=lim_{n oinfty} dfrac{5cdotleft(sqrt{1+frac{7}{n}}+1 ight)}{7} = frac{5cdot2}{7} =frac{10}{7}[/latex]