Proving series is convergent/divergent

[abcde149149]

Homework Statement

The problem is proving that the following series is convergent or divergent:

∞
Ʃ 1 / [(n)(n+1)(n+2)]^(1/3)
n=1

Homework Equations

The limit or direct comparison test

The Attempt at a Solution

lim {1 / [(n)(n+1)(n+2)]^(1/3)} / (1/n)
n->∞

I then attempted to simplify this and use l'Hopital's Rule, but the cube root made it too complicated, and I couldn't come to an answer.

 

[Dick]

Homework Statement

The problem is proving that the following series is convergent or divergent:

∞
Ʃ 1 / [(n)(n+1)(n+2)]^(1/3)
n=1

Homework Equations

The limit or direct comparison test

The Attempt at a Solution

lim {1 / [(n)(n+1)(n+2)]^(1/3)} / (1/n)
n->∞

I then attempted to simplify this and use l'Hopital's Rule, but the cube root made it too complicated, and I couldn't come to an answer.

l'Hopital is serious overkill. (n)(n+2)(n+2)=n^3(1)(1+1/n)(n+2/n). Try simplifying.