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[tex]\sum_{n=1}^{\infty}\frac{n^n}{n!}x^n[/tex]

II.

[tex]\prod_{n=1}^{\infty}n^x*sin\frac{1}{n^x}[/tex]

I wonder how to find ranges of real values [itex]x[/itex] for convergence to occur in the problems ??

**Remark about infinite product:**It is said to be convergent if partial products converge to a FINITE and NON-ZERO limit.