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x=2014 => x+1 = 2015
f(2014) = x^17 - (x+1)x^16 + ... + (x+1)x -1
= x^17 - x^17 - x^16 + x^16 - x^15 - ... + x^2 + x -1
= x - 1 = 2013
Ta thấy \(x=2014\Rightarrow x+1=2015\)
Ta có: \(f\left(2014\right)=x^{17}-\left(x+1\right)x^{16}+\left(x+1\right)x^{15}-...+\left(x+1\right)x-1\)
\(=x^{17}-x^{17}-x^{16}+x^{16}+x^{15}-...+x^2+x-1\)
\(=x-1\)(1)
Thay x=2014 vào (1) ta được:
\(f\left(2014\right)=2014-1\)
\(=2013\)
![](https://rs.olm.vn/images/avt/0.png?1311)
P(x) = x2016 - 2015x2015 - 2015x2014 - ... - 2015x2 - 2015x
<=> P(x) = x2016 - 2016x2015 + x2015 - 2016x2014 + x2014 - ... - 2016x2 + x2 - 2016x + x
<=> P(2016) = 20162016 - 2016.20162015 + 20162015 - 2016.20162014 + 20162014 -...- 2016.20162 + 20162 - 2016.2016 + 2016
<=> P(2016)=20162016 - 20162016 + 20162015 - 20162015 + 20162014 - ... - 20163 + 20162 - 20162 + 2016
<=> P(2016) = 2016
Vậy P(2016) = 2016
Ta có:
P(2016) = 20162016 - 2015 . 20162015 - 2015 . 20162014 -.....- 2015 . 20162 - 2015 . 2016 - 1
P(2016) = 20162016 - ( 2016 - 1 ) . 20162015 - ( 2016 -1 ) . 20162014 - ..... - ( 2016 - 1 ) . 20162 - ( 2016 - 1 ) . 2016 - 1
P(2016)= 20162016 - 20162016 + 20162015 - 20162015 + 20162014 - ..... - 20163 + 20162 - 20162 + 2016 - 1
P(2016) = 2016 - 1
P(2016) = 2015.
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :\(x=2014\Rightarrow2015=x+1\)
\(\Rightarrow f\left(2014\right)=x^{17}-\left(x+1\right)x^{2016}+\left(x+1\right)x^{2015}-.....+\left(x+1\right)x-1\)
\(=x^{17}-x^{17}-x^{2016}+x^{2016}+x^{2015}-....+x^2+x-1\)
\(=x-1=2014-1=2013\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Xin lỗi nha.\(x^{10}-2015x^9-2015x^8-2017x^7-...-2015x-1\)