Question

[phùng Thu Trang]

Cho P(x) = \(x^{99}\)- 100\(x^{98}\)+100\(x^{97}\)- 100\(x^{96}\)+ ... + 100x - 1 

tính P(99)

Answer 1

[๖²⁴ʱTú❄⁀ᶦᵈᵒᶫ]

Ta có : \(x=99\Rightarrow x+1=100\)

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

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

\(\Leftrightarrow x-1\) Thay x = 99 vào x - 1 ta có 

\(\Leftrightarrow P\left(99\right)=99-1=98\)