Lời giải:
lim$\frac{1^2+2^2+...+n^2}{n.(n^2+11)}$
=lim$\frac{n.(n+1).(2n+1)}{6n.(n^2+11)}$
=lim$\frac{(n^2+n).(2n+1)}{6n^3+66n}$
=lim$\frac{2n^3+3n^2+n}{6n^3+66n}$
=lim$\frac{2n^3(1+\frac{3}{2n}+\frac{1}{2n^2})}{6n^3(1+\frac{11}{n^2})}$
=lim$\frac{2n^3}{6n^3}$
=$\frac{2}{6}$
=$\frac{1}{3}$