# It must not exist.

**Calculus**Level 2

When \(n\) is natural, what is the value of

\[ \lim_{n \rightarrow \infty} ( -1 ) ^{n-1} \sin ( \pi \sqrt{ n^2 + 0.5 n + 1 } ) ?\]

When \(n\) is natural, what is the value of

\[ \lim_{n \rightarrow \infty} ( -1 ) ^{n-1} \sin ( \pi \sqrt{ n^2 + 0.5 n + 1 } ) ?\]

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