Question

Rút gọn biểu thức sau

(2018²⁰¹⁹+2018²⁰¹⁸+...+2018²+2018)2017+1

Answer 1

\(M=\left(2018^{2019}+2018^{2018}+...+2018^2+2018\right)2017+1\)

Gọi \(A=2018^{2019}+2018^{2018}+...+2018^2+2018\)

\(\Rightarrow2018A=2018^{2020}+2018^{2019}+...+2018^3+2018^2\)

\(\Rightarrow2018A-A=2018^{2020}-2018\)

\(\Rightarrow2017A=2018^{2020}-2018\)

\(\Rightarrow A=\left(2018^{2020}-2018\right)\div2017\)

\(\Rightarrow M=\left(2018^{2020}-2018\right)\div2017.2017+1\)

\(\Rightarrow M=2018^{2020}-2018+1\)

\(\Rightarrow M=2018^{2020}-2017\)