$\lim\limits_{n \rightarrow \infty} \frac{n^2\left(1^3+2^3+.....+n^3\right)}{\left(1^2+2^2+.....+n^2\right)^2}$

9/2 3/4 9/4 1/4

9/4

$\lim\limits_{x \rightarrow \infty} \frac{n^2\left[\frac{n(n+1)}{2}\right]^2}{\left[\frac{n(n+1)(2 n+1)}{6}\right]^2}=\frac{9}{4}$ Hence (3) is the correct answer.