Determine whether the series is convergent or divergent

[Hypnos_16]

Homework Statement

I have to find whether the following is Convergent or Divergent

∑ from n = 1 to infinity
2 / n(2n + 2)^(1/4)

Actually it's the fourth root, this is just easier to write.

Homework Equations

According to the front of the sheet it's a quiz on P-Series and Integral Test
I'm leaning more towards Integral Test.

The Attempt at a Solution

Not sure how to go about it, i think I've been looking at them for too long, i can't seem to remember how to do integrals anymore

 

[vela]

I wouldn't use the integral test.

 

[HallsofIvy]

Either one will work. The "P-series" test says that a series of the form \sum n^p will converge if p< 1, diverge if p\ge 1. This is not exactly of that form, but you can use the comparison test also. Can you find a p so that 1/(n(2n+2)^{1/4}&lt; n^p? The integral test says that a series \sum a_n converges if the integral \int_1^\infty a(x)dx converges where "a(x)" is just a_n with "n" replaced by "x". Can you integrate
\int_1^\infty \frac{1}{x(x+1)}dx?