<s>[INST] Is the sequence $\left\{\frac{2^n}{n!}\right\}$ convergent? If so, what is the limit? Is the sequence $\left\{\frac{2^n}{n!}\right\}$ convergent? If so, what is the limit? 
$$ \frac{2^n}{n!} - 0 = \frac{2^n}{n!} < \frac {2^n}{n} <\; ? < \epsilon$$
I dont know  how to simplify $\frac{2^n }{ n}$.
I cannot just do $\frac{2^n}{n}<\epsilon$ right ? 
 [/INST] $\frac{2^n}{n!} = \frac{2}{1} \cdot \frac{2}{2} \cdot\frac{2}{3} \cdot\frac{2}{4} \cdot\frac{2}{5}  \dots \frac{2}{n}  < \frac{2}{1} \cdot \frac{2}{2} \cdot\frac{2}{3} \cdot\frac{2}{4} \cdot\frac{2}{4}  \dots \frac{2}{4} = \frac{8}{6}\cdot(\frac{1}{2})^{n-3}$
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