Re: Monotone Convergence Question

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 09/26/04 

Date: 25 Sep 2004 19:40:42 -0500

In article <83r9l09f4hhre3aa7ejstbhp6psst78k3r@4ax.com>,
Xevious <ltcomdippy@aol.com> wrote:
>Why is the sequence (x_n) = (1-1/n)^n, bounded and monotone
>increasing?

One can use calculus.

Alternatively, if y_n = (1 - a/n)^{-n}, one can show,
as Newton did, that if 0 < |a| < n,

        y_n = \sum (a/n)^k*C(n+k-1,k),

and every term is decreasing in n if a > 0. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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