# converge or diverge?

• Feb 1st 2010, 06:08 PM
thatloserrsaid
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.
• Feb 1st 2010, 06:10 PM
skeeter
Quote:

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
• Feb 1st 2010, 06:11 PM
thatloserrsaid
the integral test confuses me.. thats why i requested a step by step help
• Feb 1st 2010, 06:12 PM
thatloserrsaid
Quote:

Originally Posted by skeeter
use the integral test

the integral test confuses me.. thats why i requested a step by step help
• Feb 1st 2010, 06:24 PM
skeeter
Quote:

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.
• Feb 1st 2010, 06:37 PM
thatloserrsaid
Quote:

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
• Feb 1st 2010, 06:38 PM
General
Quote:

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 $\displaystyle n\geq e$
• Feb 1st 2010, 08:17 PM
Pulock2009
D'Alembert's test