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




Re: Limit n^(1/n) = ? when n approaches +infinite
Posted:
Dec 19, 2004 8:34 PM


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) life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218ck (lapsed) Affiliations for identification only.
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