1) \(x+2\cdot x+3\cdot x+4\cdot x+...+2016\cdot x=2016\cdot2017\)
\(=x\cdot\left(2+3+4+...+2016\right)=4066272\)
\(=x\cdot2033136=4066272\)
\(\Rightarrow x=\frac{4066272}{2033136}=2\)
2) \(x-2\cdot x+3\cdot x-4\cdot x+...-2016\cdot x=2016\cdot2017\)
\(x\cdot\left\{\left(-2+\left(-4\right)+\left(-6\right)+...+\left(-2016\right)\right)+\left(1+3+5+7+...+2015\right)\right\}=4066272\)
\(x\cdot\left\{\left(-1017072\right)+1016064\right\}=4066272\)
\(x\cdot\left(-1008\right)=4066272\)
\(\Rightarrow x=-\frac{4066272}{1008}=-4034\)
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