I need help to determine if
$\displaystyle \frac{ln n}{n}$
converges or diverges. By the nth term test it equals 0 so it could be either. I remember doing this in class but I forgot.
To determine the convergence of $\displaystyle \sum_{n=1}^{\infty}\frac{\ln(n)}{n}$ you can do a couple things.
1) Use the integral test which states that if $\displaystyle a_n$ is continuous, nonincreasing, and positive that $\displaystyle \sum_{n=c}^{\infty} a_n $ and $\displaystyle \int_c^{\infty} f~dx$ share convergence
2) Use Cauchy's condensation test. Once again if the same hypotheses apply then $\displaystyle \sum a_n$ and $\displaystyle \sum a_{2^n}\cdot 2^n$ share convergence.