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+--- Thread: Add 1 Then Reciprocate and Fibonacci Numbers (/thread-5137.html)
Add 1 Then Reciprocate and Fibonacci Numbers - Eddie W. Shore - 11-15-2015 07:18 PM
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/the-series-0-1-1-1-1-1-1-1-1-1-1-1-1.html
RE: Add 1 Then Reciprocate and Fibonacci Numbers - Thomas Klemm - 11-16-2015 02:39 AM
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