limlimits_n → ∞ (n^2≤ft(1^3+2^3+.....+n^3))/(≤ft(1^2+2^2+.....+n^2)^2)

$\lim\limits_{x \rightarrow \infty} \frac{n^2\left[\frac{n(n+1)}{2}\right]^2}{\left[\frac{n(n+1)(2 n+1)}{6}\right]^2}=\frac{9}{4}$

Hence (3) is the correct answer.