# estimating (ln (n))/n

**URL:** <https://boards.straightdope.com/t/estimating-ln-n-n/361219>\
**Category:** Factual Questions\
**Created:** [June 18, 2006, 11:20pm UTC](https://boards.straightdope.com/t/estimating-ln-n-n/361219 "2006-06-18T23:20:59Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Larry\_Borgia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/larry_borgia/32/156_2.png) [@Larry\_Borgia](https://boards.straightdope.com/u/Larry_Borgia)\
**Post date:** [June 18, 2006, 11:20pm UTC](https://boards.straightdope.com/t/estimating-ln-n-n/361219/1 "2006-06-18T23:20:59Z")

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Suppose I’m trying to show that the series SIGMA ln(n)/n[sup]3[/sup] converges. Then I want to estimate ln(n)/n. How should I do this? Is it permissible to use the Taylor polynomial for ln(x)?

Thanks.

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**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\
**Post date:** [June 19, 2006, 1:48am UTC](https://boards.straightdope.com/t/estimating-ln-n-n/361219/2 "2006-06-19T01:48:00Z")

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> [@Larry Borgia](#):
>
> Suppose I’m trying to show that the series SIGMA ln(n)/n[sup]3[/sup] converges. Then I want to estimate ln(n)/n. How should I do this? Is it permissible to use the Taylor polynomial for ln(x)?
> 
> Thanks.

L’Hospital’s rule is your friend.

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**Author:** ![Larry\_Borgia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/larry_borgia/32/156_2.png) [@Larry\_Borgia](https://boards.straightdope.com/u/Larry_Borgia)\
**Post date:** [June 19, 2006, 2:07am UTC](https://boards.straightdope.com/t/estimating-ln-n-n/361219/3 "2006-06-19T02:07:13Z")

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> [@OldGuy](#):
>
> L’Hospital’s rule is your friend.

Thanks. For some reason I was thinking that rule only applied when the limits of the two functions both approached zero. After looking at a different text, I see that’s not true. That makes things a lot easier.