Cho hàm số y=f(x)= $x^{99}$ – 100$x^{98}$ – 100$x^{97}$ – 100$x^{96}$ +…+100x-1. Tính f(99)
Cho hàm số y=f(x)= $x^{99}$ – 100$x^{98}$ – 100$x^{97}$ – 100$x^{96}$ +…+100x-1. Tính f(99)
By Madeline
By Madeline
Cho hàm số y=f(x)= $x^{99}$ – 100$x^{98}$ – 100$x^{97}$ – 100$x^{96}$ +…+100x-1. Tính f(99)
Đáp án: $y=98$
Giải thích các bước giải:
Ta có:
$y=f(99)=99^{99}-100.99^{98}+100.99^{97}-100.99^{96}+…..+100.99-1$
$=99^{99}-99.99^{98}-99^{98}+99.99^{97}+99^{97}-99.99^{96}-…..+99.99+99-1$
$=99^{99}-99^{99}-99^{98}+99^{98}+99^{97}-99^{97}-…..+99^2+98$
$=98$
Đáp án:
y=f(x)=$x^{99}$-100$x^{98}$+100$x^{97}$-100$x^{96}$+…+100x-1
f(99)=$x^{99}$-(99+1)$x^{98}$+(99+1)$x^{97}$-(99+1)$x^{96}$+…+(99+1)x-1
f(99)=$x^{99}$-$x^{99}$-$x^{98}$+$x^{98}$+$x^{97}$-$x^{97}$-$x^{96}$+…+$x^{2}$+$x$-1
f(99)=99-1
f(99)=98