Question

A = x¹⁷- 2004.x¹⁶ + 2004.x¹⁵ - 2004.x¹⁴ +...+2004.(x - 1)

Tính A tại x = 2003

Answer 1

Thay \(x=2003\) vào A ta có:\(A=2003^{17}-2004.2003^{16}+2004.2003^{15}-2004.2003^{14}+...+2004.\left(2003-1\right)\)

\(=2003^{17}-\left(2003+1\right).2003^{16}+\left(2003+1\right).2003^{15}-\left(2003+1\right).2003^{14}+...+\left(2003+1\right).\left(2003-1\right)\)

\(=2003^{17}-2003^{17}+2003^{16}-2003^{16}+2003^{15}-2003^{15}+2003^{14}-2003^{14}+...+\left(2003+1\right).\left(2003-1\right)\)

\(=2004.2002=4012008\)