# But there's so many terms

Calculus Level 3

$\large \lim_{n\to\infty} \frac{n^k \sin^2(n!) }{n+2}$

For variable $$0<k<1$$ independent of $$n$$, let $$A$$ denote the value of the limit above, which is a non-negative integer. Evaluate $$A!$$.

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