Question 25
Let $\displaystyle A=\sum_{k=0}^{1005}\left(\binom{2010}{k}-\binom{2010}{k-1}\right)^2$. Determine the minimum integer $s$ such that $sA\ge\binom{4020}{2010}$. For a positive integer $n$, define $\binom nr=n!/(r!(n-r)!)$ when $0\le r\le n$, and $\binom nr=0$ for all other $r$.