希望杯 Basic
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}

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