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What real number is equal to the expression \(2 + \frac{1}{1 + \frac{1}{2 + \frac{1}{1 + \cdots}}}\), where the 1s and the 2s alternate?

 Nov 23, 2020
 #1
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Treat this as follows:   \(x = 2+\frac{1}{1+\frac{1}{x}}\)

 

or   \(x =2+\frac{x}{1+x}\)

 

Rearrange this to obtain a quadratic equation in x and solve for x (only the positive solution will apply).

 Nov 23, 2020

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