$$\lim_{n \to \infty} \frac{(1^2 - 1)(n-1) + (2^2 - 2)(n-2) + \cdots + ((n-1)^2 - (n-1)) \cdot 1}{(1^3 + 2^3 + \cdots + n^3) - (1^2 + 2^2 + \cdots + n^2)}$$ is equal to :

A

$$\frac{2}{3}$$

B

$$\frac{1}{3}$$

C

$$\frac{3}{4}$$

D

$$\frac{1}{2}$$