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Topic: Limit n^(1/n) = ? when n approaches +infinite
Replies: 6   Last Post: Dec 21, 2004 12:13 AM

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Kevin Karplus

Posts: 5
Registered: 12/6/04
Re: Limit n^(1/n) = ? when n approaches +infinite
Posted: Dec 19, 2004 8:34 PM
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In article <sunbs09dd8kjc3f0dgstvmsvcbhk5g55jt@4ax.com>, str wrote:
> limit n^(1/n) = ? when n approaches +infinite
> The answer is 1.
> How come?
> I think it for a long time. I cannot solve it.
> Can someone help me or give me a hint?
> I really want to know the solution.

n^(1/n) = e^ (ln(n)/n)

lim n->+infinity e^(ln(n)/n) = e^ lim n->+infinity ln(n)/n
= e ^ 0
= 1

Note: I skipped the most important step, proving that ln(n)/n -> 0 as
n -> +infinity.

Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus
Professor of Biomolecular Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
(Senior member, IEEE) (Board of Directors, ISCB starting Jan 2005)
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