Question

Cho:

a,f(x)=x¹⁰⁰ +x⁹⁹+x⁹⁸+...+x²+x+1

Tính f(2),f(-2)

b,g(x)=x+x³+x⁵+..+x¹⁰¹

Tính g(1),g(-1),g(3)

Answer 1

a) Ta có: f(x) = x¹⁰⁰+x⁹⁹+x⁹⁸+...+x+1

=>2f(x) = x¹⁰¹+x¹⁰⁰+x⁹⁹+...+x+1

=>f(x) = 2f(x)-f(x)=(x¹⁰¹+x¹⁰⁰+...+x+1)-(x¹⁰⁰+x⁹⁹+...+x+1)= x¹⁰¹-1

=>f(2) = 2¹⁰¹-1

=>f(-2) = (-2)¹⁰¹-1

b)câu còn lại tự giải :D

Answer 2

f(x) = x100+x99+x98+...+x+1

=>2f(x) = x101+x100+x99+...+x

=>f(x) = 2f(x)-f(x)=(x101+x100+...+x)-(x100+x99+...+x+1)= x101-1

=>f(2) = 2.101-1 = 201

=>f(-2) = (-2)101-1 = -203

Answer 3

chết lộn vậy mới đúng:

Ta có f(2) = \(2^{100}+2^{99}+2^{98}+...+2+1\)

=>f(2) = \(2^{101}+2^{100}+2^{99}+2^{98}+...+2\)

=>f(2) = 2f(2)-f(2)=(\(2^{101}+2^{100}+2^{99}+2^{98}+...+2\))-\(\left(2^{100}+2^{99}+2^{98}+...+2+1\right)\)=\(2^{101}-1\)