SMO 2019 Open Round 1 Question 10

Let $\{a_n\}$ be an infinite sequence with $a_1=2$ and $a_{n+1}=a_n+4n+2$ for all $n\ge1$. Determine $$\lim_{n\to\infty}2000\left(\frac1{a_2-2}+\frac1{a_3-2}+\cdots+\frac1{a_n-2}\right).$$