Add 1 Then Reciprocate and Fibonacci Numbers - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: Not HP Calculators (/forum-7.html) +--- Forum: Not remotely HP Calculators (/forum-9.html) +--- 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