2013
Problem - 3161
Suppose function $f(x)=\frac{1+x}{1-x}$. Evaluate $$f\Big(\frac{1}{2}\Big)\cdot f\Big(\frac{1}{4}\Big)\cdot f\Big(\frac{1}{6}\Big)\cdots f\Big(\frac{1}{2014}\Big)$$
\begin{align}
& f\Big(\frac{1}{2}\Big)\cdot f\Big(\frac{1}{4}\Big)\cdot f\Big(\frac{1}{6}\Big)\cdots f\Big(\frac{1}{2014}\Big)\\
=&\frac{3}{1}\times\frac{5}{3}\times\frac{7}{5}\times\cdots\times\frac{2015}{2013}\\
=&\boxed{2015}
\end{align}