estimating (ln (n))/n

Suppose I’m trying to show that the series SIGMA ln(n)/n[sup]3[/sup] converges. Then I want to estimate ln(n)/n. How should I do this? Is it permissible to use the Taylor polynomial for ln(x)?


L’Hospital’s rule is your friend.

Thanks. For some reason I was thinking that rule only applied when the limits of the two functions both approached zero. After looking at a different text, I see that’s not true. That makes things a lot easier.