It has probably been answered before on MHF, but I didn't find it using the search button.

Tell whether the following infinite series is convergent or not :

. At first, I used the ration test, but I cannot conclude since it says "1". Then the integral test, which gave me divergent, but I'm not sure I did it well, because when I tried to get an approximation via Mathematica, I got an error like if it converges, it does it too slow or something like that. Nevertheless, it said an approximation is 13.4391. From it I doubted my integral test was well made. I tried the root test, but I'm not sure how to finish it.

Integral test :

. Let

be

, then

, and the integral becomes

. Replacing

by

, it's easy to see the integral diverges.

So normally, so does the infinite series. Am I right?