We can take this function

we
get _{}. Then we'll put
^{ }in for x again, and we get . If we keep doing that we get this **infinite
continued fraction**. Jonathan, at age 7, did this at home with his
Mom. He got all excited about this being infinite!

If you put 1 in the
first of these you get ^{-}1. If you put 1 in the second one you get 11. If
you put 1 in for x in the third one you get 4.4545.. You get an infinite
sequence which approaches 3, which is one of the two roots of the
equation.

If you start with -100, you would still get an infinite sequence approaching 3 as well. Notice, you only get the one root, 3, using method 2.

To order Don's materials

Back to Ch. 8, part 2- iteration

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