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MathGroup Archive 2000

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Re: Limit problem from analysis

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21582] Re: Limit problem from analysis
  • From: "N. Shamsundar" <shamsundar at uh.edu>
  • Date: Sat, 15 Jan 2000 02:04:25 -0500 (EST)
  • Organization: MECE-4792, University of Houston
  • References: <85i0pc$1ph@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

This is really not a Mathematica question, since you could ask
for Limit[n^(1/n),n->Infinity]
and receive the answer.

Let n=1/(1-x), then n^n=(1-x)^{-(1-x)}.  Expand using the
binomial theorem, which is valid for |x| < 1. Take limits as
x->1.

N. Shamsundar
University of Houston

world at writemaster.com.xxx wrote:
> 
> I am teaching myself analysis, and I'm stuck on a particular problem.
> The problem is to prove that the limit as n goes to infinity of n to
> the (1/n) power is 1.  The only allowed tools are those of the first
> few chapters of a basic analysis textbook.  The hint given in the book
> is to use the binomial theorem.
> 
> You can find the work I've done at
> http://writemaster.com/public/mathPostings/
> There are two documents there, one a Mathematica notebook and the
> other an MS Word document.   Any suggestions for how to proceed, or
> even outright solutions, would be welcome.
> 
> I am not taking any classes, and you will not be helping me with a
> test or homework.
> 
> Steve Oppenheimer
> writer at writemaster.com


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