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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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