If $x = 1 + \frac{x}{1 + \frac{x}{1+ \frac{x}{1 + \cdots}}}$, then what is $x$?
+96 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.
+96 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.
