Confirming Convergence: $\sum \frac{(-1)^{n+1}(n^2+4)^{1/3}}{(n^5+1)^{1/2}}$

[duki]

Homework Statement

\sum \frac{(-1)^{n+1}(n^2+4)^{1/3}}{(n^5+1)^{1/2}}

Homework Equations

The Attempt at a Solution

I got that it converges, because the limit is 0
Is that right?

 

[Mark44]

You apparently are using the alternating series test. Have you established all of the following?
The a_n's are all positive.
a_n >= a_(n+1) for all n.
lim a_n = 0, as n approaches infinity.