Question 219498
Let *[Tex \LARGE y = 2+\frac{3}{2+\frac{3}{2+...}}]


Take note how the bottom portion of the fraction is *[Tex \LARGE 2+\frac{3}{2+...}] which is equal to 'y' (continue it out and you'll see it). I.e. the same expression is nested inside the larger expression. 




This means that 


*[Tex \LARGE y = 2+\frac{3}{2+\frac{3}{2+...}}=2+\frac{3}{y}]



Or in short


*[Tex \LARGE y=2+\frac{3}{y}]



Now just solve for 'y' to find the value of *[Tex \LARGE 2+\frac{3}{2+\frac{3}{2+...}}]


Note: you will get two solutions, but you're only going to focus on the positive solution.