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?
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).
