Re: recursion on TI-86 (correction)

To: CALC-TI@LISTS.PPP.TI.COM
Subject: Re: recursion on TI-86 (correction)
From: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>
Date: Mon, 21 Dec 1998 12:19:00 -0500
Reply-To: RWW Taylor <RWTNTS@RITVAX.ISC.RIT.EDU>

Having gotten to the office and taken a direct look at my TI-86 (and manual)
I find a few differences from the hypothetical suggestion I posted here a few
hours ago, plus a built-in convenience that simplifies matters somewhat. In
particular, being able to store an element into the "one past the end" position
in an existing list in order to extend it means that you don't have to create
in advance entries to fill. Also, the TI-86 uses parentheses rather than
brackets to index lists (why can't we get together on this, guys?). Plus the
lower-case letter n is _reserved_, and can't be freely used as a variable.

So, all this said, here's what you can do to generate the list in question:

1-->m : {2}-->aa   <ENTER>
m+1--m : aa(m-1) + 4/aa(m-1)-->aa(m) <ENTER>

Press ENTER ad lib to generate additional terms.

This turns out to be a non-trivial exercise -- successive terms generated
are strictly increasing and (it can be shown) divergent. What the terms are
around m=1000 is not something that can be easily predicted, as I had at first
suspected.

This particular recursion is intimately linked with sums that can be (and often
are) generated iteratively. You can also generate this sequence directly by
using the TI-86's cSum( command.

RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623

>>>> The plural of mongoose begins with p. <<<<