Add 1 Then Reciprocate and Fibonacci Numbers

11152015, 07:18 PM
Post: #1




Add 1 Then Reciprocate and Fibonacci Numbers
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...111.html 

11162015, 02:39 AM
Post: #2




RE: Add 1 Then Reciprocate and Fibonacci Numbers
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 

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