Add 1 Then Reciprocate and Fibonacci Numbers

[Eddie W. Shore]

The Series ( ((((0 + 1)^-1 + 1)^-1 + 1)^-1 + 1)^-1 + 1)^-1 + … + 1)^-1 and Fibonacci Numbers.

I used the HP Prime to help me with this blog entry, in programming, plotting, and the CAS functions.

http://edspi31415.blogspot.com/2015/11/t...1-1-1.html

[Thomas Klemm]

You can calculate the limes as the fixed point of the iteration:
\[
x=\frac{1}{x+1}
\]
This results in:
\[
x^2+x=1
\]
There are two solutions. One of them is attractive: \(\frac{\sqrt{5}-1}{2}\approx 0.61803\).

Cheers
Thomas