# Ratio Test of Convergence

• Feb 26th 2010, 02:18 PM
featherbox
Ratio Test of Convergence
I have to decide whether a the summation of a function over [1,infinty) converges or not.
A particular function is troubling me

$\frac{ln(n)}{n^3}$

I figured the Ratio test would be the best way to go about this. But I got

$\frac{a_{n+1}}{a_{n}} \rightarrow 1$

but seeing as 1 is not <1 or >1, so the test is inconclusive, yes?

Where would I proceed from here? Does this mean the limit does not exist, hence divergent?
• Feb 26th 2010, 02:30 PM
Plato
Quote:

Originally Posted by featherbox
I have to decide whether a the summation of a function over [1,infinty) converges or not.
A particular function is troubling me

$\frac{ln(n)}{n^3}$

Use the comparison test.
You know that $\ln(n).
• Feb 26th 2010, 02:37 PM
featherbox
of course! Thanks.
That's so simple haha.
Can't believe I missed that.