Question

[Đào Thị Thu Hương]

 tìm chữ số tận cùng a=2¹⁰+2¹¹+2¹²+...+2²⁰¹⁸

Answer 1

[Nguyễn Võ Anh Nguyên]

\(A=2^{10}+2^{11}+2^{12}+...+2^{2018}\)

\(2A=2^{11}+2^{12}+2^{13}+...+2^{2019}\)

\(2A-A=A=2^{2019}-2^{10}=2^{2016}.2^3-2^8.2^2=\overline{...6}.8-\overline{...6}.4=\overline{...8}-\overline{...4}=\overline{...4}\)