# Determine whether the series is convergent or divergent

## 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
Staff Emeritus
Homework Helper
I wouldn't use the integral test.

HallsofIvy
Homework Helper
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 $1/(n(2n+2)^{1/4}< n^p$? 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
$$\int_1^\infty \frac{1}{x(x+1)}dx$$?