converge or diverge?

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February 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.
February 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
February 1st 2010, 06:11 PM
thatloserrsaid

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

$\int_2^{\infty} \frac{\ln{x}}{x} \, dx$

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

give it a go.
February 1st 2010, 06:37 PM
thatloserrsaid

Quote:

Originally Posted by skeeter

$\int_2^{\infty} \frac{\ln{x}}{x} \, dx$

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

give it a go.

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

$\frac{ln(n)}{n}\geq\frac{1}{n}$ for $n\geq e$
February 1st 2010, 08:17 PM
Pulock2009

1 Attachment(s)

D'Alembert's test

please see attachment:

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