Problem

Part III Solve the following problems

17. Given a family of parabolas $P_n:y=nx^2+\dfrac{1}{n}$, where $n\in\mathbb{N}$. Let $A_n$ be the area between $P_n$ and $P_{n+1}$. Find the limit $\lim_{n\to\infty}\dfrac{A_n}{n^3}$.