It must not exist.

Calculus Level 2

When nn is a positive integer, what is the value of

limn(1)n1sin(πn2+0.5n+1)? \lim_{n \rightarrow \infty} ( -1 ) ^{n-1} \sin ( \pi \sqrt{ n^2 + 0.5 n + 1 } ) ?

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