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From: franka@mmintl.UUCP (Frank Adams)
Newsgroups: net.math
Subject: Re: Pascal's Inverse Triangle
Message-ID: <481@mmintl.UUCP>
Date: Fri, 12-Jul-85 14:06:07 EDT
Article-I.D.: mmintl.481
Posted: Fri Jul 12 14:06:07 1985
Date-Received: Mon, 15-Jul-85 00:40:24 EDT
References: <2216@utcsstat.UUCP> <1677@saber.UUCP> <788@wanginst.UUCP>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Organization: Multimate International, E. Hartford, CT
Lines: 13
Summary: Center terms approach limit



The center terms of the inverse triangle approach 1/sqrt(2).  This can be
seen by noting that, assuming that a limit x is approached, x = 1/(x + x).
Algebra gives us the result stated.  This isn't a formal proof, but it
can be extended to one.

Generally, each column converges to a distinct limit.  If a column converges
to a, the next column will converge to b = 1/(a + b), which when solved
gives b = (-a + sqrt(a^2 + 4)) / 2.  The first case is a = 1 and
b = (-1 + sqrt(5))/2; generally we get a nested sequence of square roots.

These results are quite straightforward.  Off hand, I see no approach
to getting any deeper results.  This seems to be any interesting problem.