Let $u_n=n^2$ be an explicitly defined sequence.

1. By considering $u_{n+1}-u_n,$ write $u_n$ in terms of a recursive formula.

2. Hence, or otherwise, find the value of

   $$1+3+5+7+\dots +999+1001$$

Note that $u_{n+1}=(n+1{)}^2$

For (b), notice that