$\displaystyle a_n = \frac{5n!}{2^n} $
I don't understand why this sequence is divergent. Any help is much appreciated.
Sorry, I should've rephrased my question. I don't understand how to prove that the sequence is divergent. My solutions manual shows this:
$\displaystyle a_n = \frac{5n!}{2^n} = \frac{5}{2} \times \frac{2}{2} \times \frac{3}{2} \times \frac{4}{2} ... \frac{n-1}{2} \times \frac{n}{2} \geq \frac{5}{2} \times \frac{n}{2} \ \ for\ n > 2 = \frac{5n}{4} \rightarrow \infty, so\ {a_n}\ diverges. $
But I don't understand what they did.