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