Will the answer change?

Calculus Level 5

$\large \lim_{n \to \infty} \left | \cos\left( \dfrac{\pi \sqrt{n^2+n}}{2} \right) \right |$

What is the value of the limit above for integers $n$ ? Give your answer up to 3 decimal places.

Submit $12345$ as the answer if the limit does not exist.