Simple series question.

1. Nov 1, 2007

azatkgz

Determine whether the series $$\sum_{n=2}^{\infty}a_n$$ converges absolutely,converges conditionally or diverges.If

$$a_n=\frac{1+n+n^2}{\sqrt{1+n^2+n^6}}$$

For several n I get $$a_n>\frac{1}{n}$$ so I decided that this series is divergent.Right?

2. Nov 1, 2007

Dick

That would do it. But did you prove that inequality? Just looking at 'several n' basically means you are guessing.

3. Nov 2, 2007

Gib Z

In fact the result can be much weaker, we don't need to prove the inequality for all n, or even that a_n is more than 1/n, just equal. Divide the terms through by n^2 and see what the n-th term as n --> infinity is.