Series + Integral: Investigate Convergence

[asi123]

Homework Statement

Hello.

I need to to investigate (I hope I said that right ) the converge of this function, any idea guys?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

I would recommend using the "ratio test". That will lead to an integral from 1/(n+1) to 1/n and you need to show that the limit of that integral, as n goes to infinity, is less than 1.

 

[Gib Z]

$$\lim_{n\to \infty} \frac{ \int^{1/{n+1}}_0 \frac{x^{1/4}}{1+x^2} dx}{ \int^{1/{n}}_0 \frac{x^{1/4}}{1+x^2} dx}$$.

I'm not sure how that gives an integral from 1/(n+1) to 1/n =S

EDIT: Dont know what's wrong with the latex.