+0  
 
+2
116
4
avatar+313 

Find the value of \(\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}\)

 Jul 22, 2020
 #1
avatar
0

Let \(x = \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}\)

 

Then x = 1/(x + 1) ==> x^2 + x - 1 = 0 ==> x = (sqrt(5) - 1)/2

 Jul 22, 2020
 #2
avatar+31085 
+3

I get the following:

 

 Jul 22, 2020
 #4
avatar+313 
+2

Thanks so much for your help!!!

mathmathj28  Jul 22, 2020
 #3
avatar
0

c=0;m=0;p=0;a=listfor(n, 1, 10,listforeach(m, d=reverse(1,2),(c=1/(c + m))
=Sqrt(3) - 1 = 0.7320508076

 Jul 22, 2020

54 Online Users

avatar
avatar