What is the numerical value of \( x = \frac{1}{2-\frac{1}{2-\frac{1}{2-\ldots}}} ?\)
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
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
+87 
