I was given the following question:
Determine if the following series is convergent. You may use basic series, but you should clearly state which results or rules you use.
$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}\sqrt{n}}{n+4}$
Does the Alternating Series Test require the positive term $\frac{\sqrt n}{n+4}$ to be decreasing for all $n$ or is it sufficient that the term is eventually decreasing? ($\frac{\sqrt n}{n+4}$ is decreasing only for $n>3$.)