Theo đề bài ta có
\(f\left(x\right)=x^{2017}-2016.x^{2016}+2016.x^{2015}-...+2016.x-1\)
Với \(f\left(2015\right)\)thì \(x=2015,x+1=2016\)
\(\Rightarrow f\left(x\right)=x^{2017}-\left(x+1\right).x^{2016}+\left(x+1\right).x^{2015}-...+\left(x+1\right).x-1\)
\(\Rightarrow f\left(x\right)=x^{2017}-x^{2017}-x^{2016}+x^{2016}+x^{2015}-...+x^2+x-1\)
\(\Rightarrow f\left(x\right)=x-1\)
\(\Rightarrow f\left(2015\right)=2015-1=2014\)
Vậy f(2015)=2014
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