1+4+4^2+4^3 + ......... +4^2021 chia hết cho 21
=(1+4+4²)+(4³+4^4+4^5)+..........+(4^2019+4^2020+4^2021)
=21+4³.(1+4+4²)+............+ 4^2019.(1+4+4²)
=21+4³.21+...............+ 4^2019.21
=21.( 4³+ 4^6+...........+ 4^2019)
vì 21 chia hết cho 21
⇒1+4+4^2+4^3 + ......... +4^2021 chia hết cho 21