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If $x = 1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}$, then what is $x$?

 Jun 25, 2019

Best Answer 

 #1
avatar+91 
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So, when translating to LaTeX, we get \(x = 1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}\)

Look at all the fractions under the first x. That is \(1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}\)

But that is also x! 

 

So, x = 1 + x/x which is x = 1 + 1 which is 2.

 Jun 25, 2019
 #1
avatar+91 
+2
Best Answer

So, when translating to LaTeX, we get \(x = 1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}\)

Look at all the fractions under the first x. That is \(1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}\)

But that is also x! 

 

So, x = 1 + x/x which is x = 1 + 1 which is 2.

Pushy Jun 25, 2019

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