File spoon-archives/phillitcrit.archive/phillitcrit_1997/phillitcrit.9711, message 1037


From: Patsloane-AT-aol.com
Date: Wed, 26 Nov 1997 03:44:10 -0500 (EST)
Subject: Re: PLC: Numb&Coh>>Fibonacci&Gold


Metin,

This is the beginning of the series of triangular numbers.

           1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66....

For the 4th term in the series, 10 = 0.5((4x4)+4)

For the 11th term, 66=0.5((11x11)+11)

Hope this is clear.

I checked the series of ratios between consecutive terms, and it's nothing at
all like the series of ratios between consecutive terms in the Fibonacci
series.  For one thing, the terms in the series of ratios (between
consdecutive terms in the triangular number series)   grow progressively
larger, not progressively smaller.  Also, the alternation I mentioned in my
last post isn't present. Each term in the series of ratios is larger than the
previous term.

pat



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