For a problem such as:
$ \sum_{n=1}^\infty \frac{lnn}{n^3}$
How do you tell if it is decreasing or increasing? I know that you can compute the derivative and test if it is less than or greater than zero, but the way my solutions manual does it, I'm puzzled by.
The derivative is:
$\frac{1-3lnx}{x^4} < 0$
Solving for x gives $x > e^\frac{1}{3}$.
I'm confused as to how that shows that the function is decreasing.