Đs 2005x

Thay 2000=x-6 nhé

xin loi minh ko biet nha bnxin loi minh ko biet nha bn

xin loi minh ko biet nha bn

xin loi minh ko biet nha bn

xin lỗi mình ko bik

xin lỗi minh ko bik

xin lỗi mik kobik

giả cụ thể đc ko ạ

giả cụ thể đc ko bạn mình ko làm đc

\(A=x^{30}-2000x^{29}+2000x^{28}-2000x^{27}+...+2000x^2-2000x+2000\)

Ta có: \(f\left(x\right)=x^{30}-2000x^{29}+2000x^{28}-2000x^{27}+...+2000x^2-2000x+2000\)

\(\Leftrightarrow f\left(2006\right)=2006^{30}-2000.2006^{29}+2000.2006^{28}-2000.2006^{27}+...\)\(+2000.2006^2-2000.2006+2000\)

\(\Rightarrow2006.f\left(2006\right)=2006^{31}-2000.2006^{30}+2000.2006^{29}-2000.2006^{28}+...\)\(+2000.2006^3-2000.2006^2+2000.2006\)

\(\Rightarrow2006.f\left(2006\right)+f\left(2006\right)=2006^{31}-2000.2006^{30}+2000.2006^{29}-2000.2006^{28}+...\)\(+2000.2006^3-2000.2006^2+2000.2006\)\(+2006^{30}-2000.2006^{29}+2000.2006^{28}-2000.2006^{27}+...+2000.2006^2-2000.2006+2000\)

\(\Rightarrow2007.f\left(2006\right)=2006^{31}-2000.2006^{30}+2006^{30}+2000\)

\(\Rightarrow f\left(2006\right)=\frac{2006^{31}-2000.2006^{30}+2006^{30}+2000}{2007}\)

\(\Rightarrow f\left(2006\right)=\frac{2006^{30}\left(2006-2000+1\right)+2000}{2007}\)

\(\Rightarrow f\left(2006\right)=\frac{7.2006^{30}+2000}{2007}\)

\(=x^3-\left(x-6\right)x^{29}+\left(x-6\right)x^{28}-\left(x-6\right)x^{27}+...+\left(x-6\right)x^2-\left(x-6\right)x+x-6\)

=\(x^{30}-x^{30}+6x^{29}+x^{29}-6x^{28}-x^{28}+6^{27}+...+x^3-6x^2-x^2+6x+x-6\)

=\(7\left(x^{29}-x^{28}+x^{27}+...+x^2-x\right)+6\)