Hi.

I've got a straight forward alternating series test problem:

Use the A.S.T. to determine whether the series

$\displaystyle \displaystyle\sum_{n=1}^{\infty}\frac{(-1)^n\sqrt{n^3+1}}{n^5}$

converges.

We know that $\displaystyle \displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty }\frac{\sqrt{n^3+1}}{n^5}=0$, but when we try to show that

$\displaystyle a_{n+1}\leq{a_n}$

I am having trouble with this inequality. Help?