- #1

- 4

- 0

## Homework Statement

Does the sequence {(1/2)ln(1/n)} converge or diverge?

## Homework Equations

Working it out analytically, I think it diverges. I would like to know the appropriate test to show this

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter garryh22
- Start date

- #1

- 4

- 0

Does the sequence {(1/2)ln(1/n)} converge or diverge?

Working it out analytically, I think it diverges. I would like to know the appropriate test to show this

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 966

Seems to me that you can easily show that this diverges from the original definition. I presume that your numerical calculations (I'm not sure what you mean by "analytically". If you have show analytically that this diverges, you are done.) diverges to negative infinity.

That should lead you to look at (1/2)ln(1/n)< -M for M some large integer. Then ln(1/n)< -2M so 1/n< e^{-2M[/sum] and n> eM. Working the other way, for any integer M, if n< eM then (1/2)ln(1/n)< -M and so the sequence diverges.}

That should lead you to look at (1/2)ln(1/n)< -M for M some large integer. Then ln(1/n)< -2M so 1/n< e

Last edited by a moderator:

- #3

- 26

- 0

lim n -> inf gives (1/2)ln(0) which is not defined and clearly not zero. Therefore it diverges.

Share: