Câu hỏi của Đặng Quốc Khánh ( dặt dẹo )

Question

cho f(x) = x^99 - 2017 x^98 + 2017x^97 - 2017x^96 + ..... +-2017x^2 + 2017x - 1 Tìm f ( 2016)

Phương Trâm · Accepted Answer

$f\left(x\right)=x^{99}-2017^{x^{98}}+2017^{x^{97}}-...+2017x-1$

$f\left(2016\right)=2016^{99}-2017.2016^{98}+2017.2016^{97}-...+2017.2016-1$

$f\left(2016\right)=2016^{99}-\left(2016+1\right).2016^{98}+\left(2016+1\right).2016^{97}-...+\left(2016+1\right).2016-1$

$f\left(2016\right)=2016^{99}-2016^{99}-2016^{98}+2016^{98}+2016^{97}-2016^{97}-2016^{96}+...+2016^2+2016-1$

$f\left(2016\right)=2016-1$

$f\left(2016\right)=2015$Câu trả lời: $f\left(x\right)=x^{99}-2017^{x^{98}}+2017^{x^{97}}-...+2017x-1$

$f\left(2016\right)=2016^{99}-2017.2016^{98}+2017.2016^{97}-...+2017.2016-1$

$f\left(2016\right)=2016^{99}-\left(2016+1\right).2016^{98}+\left(2016+1\right).2016^{97}-...+\left(2016+1\right).2016-1$

$f\left(2016\right)=2016^{99}-2016^{99}-2016^{98}+2016^{98}+2016^{97}-2016^{97}-2016^{96}+...+2016^2+2016-1$

$f\left(2016\right)=2016-1$

$f\left(2016\right)=2015$