For a positive integer $n$, the $n^{th}$ triangular number is $T(n)=\dfrac{n(n+1)}{2}.$ For example, $T(3) = \frac{3(3+1)}{2}= \frac{3(4)}{

For a positive integer \(n\), the \(n^{th}\) triangular number is \(T(n)=\dfrac{n(n+1)}{2}.\)

For example, \(T(3) = \frac{3(3+1)}{2}= \frac{3(4)}{2}=6\), so the third triangular number is 6.

Determine the smallest integer \(b>2011\) such that \(T(b+1)-T(b)=T(x)\) for some positive integer .