# Thread: converge or diverge?

1. ## converge or diverge?

infinity
summation of ln(n)/n
n=2

I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.

2. Originally Posted by thatloserrsaid
infinity
summation of ln(n)/n
n=2

I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.
use the integral test

3. the integral test confuses me.. thats why i requested a step by step help

4. Originally Posted by skeeter
use the integral test
the integral test confuses me.. thats why i requested a step by step help

5. Originally Posted by thatloserrsaid
the integral test confuses me.. thats why i requested a step by step help
$\displaystyle \int_2^{\infty} \frac{\ln{x}}{x} \, dx$

substitution ... let $\displaystyle u = \ln{x}$

give it a go.

6. Originally Posted by skeeter
$\displaystyle \int_2^{\infty} \frac{\ln{x}}{x} \, dx$

substitution ... let $\displaystyle u = \ln{x}$

give it a go.

after i integrate i get [ln(x)]^2 / 2

7. Originally Posted by thatloserrsaid
infinity
summation of ln(n)/n
n=2

I need to know if it converges or diverges and explain why. If someone could go though this step by step it would be a big help.
$\displaystyle \frac{ln(n)}{n}\geq\frac{1}{n}$ for $\displaystyle n\geq e$