Binomial Theorem

\(r\) and \(n\) are positive integers \(\,r > 1,\,n > 2\) and coefficient of \(\,{\left( {r + 2} \right)^{th}}\) term and \(3{r^{th}}\) term in the expansion of \({\left( {1 + x} \right)^{2n}}\) are equal, then \(n\) equals

The positive integer just greater than \({\left( {1 + 0.0001} \right)^{10000}}\) is