Problem - 3245
Compute $$\frac{1}{\frac{1}{\frac{1}{\cdots}+1+\frac{1}{\cdots}}+1+\frac{1}{\frac{1}{\cdots}+1+\frac{1}{\cdots}}}$$
Let $x=\frac{1}{\frac{1}{\frac{1}{\cdots}+1+\frac{1}{\cdots}}+1+\frac{1}{\frac{1}{\cdots}+1+\frac{1}{\cdots}}}$, then we have
$$x=\frac{1}{x+1+x}$$
Solving this equation and takes positive solution gives the answer that $x=\boxed{\frac{1}{2}}$.