# 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.