Oblicz granice: lim 2+4+6+....+2n/n^2+5n   lim (sqrt2n+3-sqrt2n)   lim (n+3)(n+1)/2n^2+4n  

1. [latex]2+4+6+...+2n}{n^2+5n}=frac{frac{2+2n}{2}cdot n}{n(n+5)}=frac{1+n}{n+5}=\=frac{frac{1}{n}+1}{1+frac{5}{n}} o_{n oinfty} frac{1}{1}=1[/latex]   2. [latex]sqrt{2n+3}-sqrt{2n}=frac{2n+3-2n}{sqrt{2n+3}+sqrt{2n}}=frac{3}{sqrt{2n+3}+sqrt{2n}} o_{n oinfty} 0[/latex]   3. [latex]frac{(n+3)(n+1)}{2n^2+4n}=frac{n^2+4n+3}{2n^2+4n}=\=frac{1+frac{4}{n}+frac{3}{n^2}}{2+frac{4}{n}} o_{n oinfty} frac{1}{2}[/latex]