Question

Does the following series converge or diverge? ∑n=1∞[(n√)÷(n2+1)]

Answer 1

The suggestion given to your earlier was exactly right. For all n,
\[ \frac{\sqrt{n}}{n^2 + 1} < \frac{\sqrt{n}}{n^2} \]
Now does the sum of the terms on the right converge? Yes. (Why?)

That being the case, it means that the original sum converges. (Why?)

You need to fill in the details.

Answer 2

"...given to you earlier was exactly right."