1: \(\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\cdots+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)
=>\(2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\cdots+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)
=>\(2\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
=>\(2\left(\frac12-\frac{1}{x+1}\right)=\frac{2013}{2015}\)
=>\(1-\frac{2}{x+1}=\frac{2013}{2015}\)
=>\(\frac{2}{x+1}=1-\frac{2013}{2015}=\frac{2}{2015}\)
=>x+1=2015
=>x=2014
2: x-y-z=0
=>x-y=z; x-z=y; x=y+z
\(P=\left(1-\frac{z}{x}\right)\left(1-\frac{x}{y}\right)\left(1+\frac{y}{z}\right)\)
\(=\frac{x-z}{x}\cdot\frac{y-x}{y}\cdot\frac{z+y}{z}=\frac{y}{x}\cdot\frac{-z}{y}\cdot\frac{x}{z}=-1\)
