+0  
 
-1
128
2
avatar+39 

What is the numerical value of \( x = \frac{1}{2-\frac{1}{2-\frac{1}{2-\ldots}}} ?\)

 Dec 10, 2019
 #1
avatar+109064 
+1

Letting x be = to the continued fraction, we have that

 

                  1

x  =   ____________                  multiply  each side by    2   - x

               2    -   x  

 

 

2x - x^2   = 1           rearrange as

 

x^2 - 2x  + 1   =  0      factor

 

(x - 1)^2  =   0          take the root

 

x  -   1   =   0

 

x  =   1

 

 

cool cool cool

 Dec 10, 2019
 #2
avatar
0

Look at the result here !! What in the world does it mean? I don't get it !!

 

https://www.wolframalpha.com/input/?i=x+%3D+%5Cfrac%7B1%7D%7B2-%5Cfrac%7B1%7D%7B2-%5Cfrac%7B1%7D%7B2-%5Cldots%7D%7D%7D%2C+solve+for+x

 Dec 10, 2019

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