\(\displaystyle [FONT=&]\sum[/FONT][FONT=&]_{n=2}^{\infty}\frac{1}{\sqrt{n*\sqrt{n-1}}}[/FONT][\math]

I don't know if i wrote that correctly, but it's essentially a series with a denominator consisting of sqrt(n(sqrt(n-1))), starting at 2 and going to infinity. The instructions for the question is to determine whether the series converges or diverges, and to state the method used. I tried splitting the denominator into n's to the powers of -1/2 and -1/4, then using the partial fractions. But my attempt was incorrect.

Does anyone have any idea how to approach this problem? I really thought I was onto something with the fractional exponents.

(Another image, just in case.)

(EDIT: yup, totally messed up the latex code. Sorry about that.)\)