Solution
= Solution
For the positive terms $a_n=n!/2^n$, the ratio is $a_{n+1}/a_n=(n+1)/2\to\infty$. The <ratio test> therefore gives divergence. More directly, the terms increase by a factor at least two for all $n\ge3$, so they fail the necessary <term test for divergence> condition $a_n\to0$. Hence
$$
\boxed{\sum_{n=1}^\infty\frac{n!}{2^n}\text{ diverges to }+\infty.}
$$