Re: Monotone Convergence Question
From: Peter L. Montgomery (Peter-Lawrence.Montgomery_at_cwi.nl)
Date: 09/25/04
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Date: Sat, 25 Sep 2004 22:29:14 GMT
In article <83r9l09f4hhre3aa7ejstbhp6psst78k3r@4ax.com>
Xevious <ltcomdippy@aol.com> writes:
>Why is the sequence (x_n) = (1-1/n)^n, bounded and monotone
>increasing?
Express x_(n+1) / x_n as a product of powers of
n-1, n, and n+1. Show that this product is > 1 when n > 1,
after replacing part of the product by a power of n^2/(n^2 - 1).
You may need the easily proved inequality
(1 + x)^n >= 1 + x*n when x >= 0 and n is an integer.
-- During a wedding ceremony, members of the audience cried. Scientists examined the tears. They determined the liquid was eye dew. pmontgom@cwi.nl Microsoft Research and CWI Home: Bellevue, WA
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