f(2016)=2016^8 - 2017*2016^7 +2017*2016^6 - 2017*2016^5 +...+2017*2016^2 - 2017*2016+ 2018

=2016^8 -( 2016^8 + 2016) + (2016^7+2016) - (2016^6 + 2016)+....+2016^3+2016 -( 2016^2 + 2016)+2018

=2018

mình đọc chả hiểu gì 

có bạn nào giải chi tiết ra được không

A=x⁸-2016x⁷-x⁷+2016x⁶+x⁶-2015x⁵+....+2017x+x-2016+2018

  =x⁷(x-2016)-x⁶(x-2016)+.....-x(x-2016)+(x-2016)+2018

Do x=2016\(\Leftrightarrow\)x-2016=0

A=2018

a/ Với \(x=2016\Rightarrow2017=x+1\)

\(A=x^6-\left(x+1\right)x^5+\left(x+1\right)x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+2025\)

\(A=x^6-x^6-x^5+x^5+x^4-x^4-x^3+x^3+x^2-x^2-x+2025\)

\(A=2025-x=9\)

b/ Với \(x=-1\Rightarrow\left\{{}\begin{matrix}x^{2k}=1\\x^{2k+1}=-1\end{matrix}\right.\) ta có:

\(Q=2017-2016+2015-2014+...+3-2+1\)

\(Q=1+1+1+...+1+1\) (có \(\frac{2016}{2}+1=1009\) số 1)

\(Q=1009\)

Dễ thầy 2017=2016+1=x+1

Thay vào ta có:

\(x^{10}-2017x^9+2017x^8-.....+2017x^2-2017x+2017\)

\(=x^{10}-\left(x+1\right)x^9+\left(x+1\right)x^8-....+\left(x+1\right)x^2-\left(x+1\right)x+2017\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-....+x^3+x^2-x^2-x+2017=-x+2017=-2016+2017=1\)

Vậy..........

thanks bn!!

456545756858768978087

Ta có: 

\(A=x^8-2017x^7+2017x^6-2017x^5+...+2017x^2-2017x+25\)

\(=\left(x^8-2016x^7\right)+\left(-x^7+2016x^6\right)+...+\left(x^2-2016x\right)-x+25\)

\(=\left(x-2016\right)\left(x^7-x^6+...+x\right)-x+25\)

Thế x = 2016 vào A ta được

\(=\left(2016-2016\right)\left(2016^7-2016^6+...+2016\right)-2016+25=-2016+25=-1991\)

A=1991

Ko biet lam quen cach lam rui hihihi ^,^

x=2016 nên x+1=2017

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

\(=x^{99}-x^{99}-x^{98}+x^{98}+x^{97}-x^{97}+...-x^3-x^2+x^2+x-1\)

=x-1=2015

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

\(=x^{99}-2016x^{98}-x^{98}+2016x^{97}+...-x^2+2016x+x-2016+2015\)

\(=x^{98}\left(x-2016\right)-x^{97}\left(x-2016\right)+...-x\left(x-2016\right)+\left(x-2016\right)+2015\)

\(=\left(x^{98}-x^{97}+...-x+1\right)\left(x-2016\right)+2015\)

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

Vậy...