$$a_{n}=\frac{2^nn!\cos\left(n^5\right)}{n^n}$$
Any ideas on this? Does it even converge?
2026-02-22 19:06:53.1771787213
Does this sequence converge? And if so to what?
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use that $$\left|\frac{2^nn!\cos(n^5)}{n^n}\right|\le \frac{2^n n!}{n^n}$$ and this tends to zero for $n$ tends to infinity