Question

1)A=1+5+5^2+5^3+...+5^2019 chia hết cho -31

Giải giúp mk nha phải chi tiết vào nha thanks mn

Answer 1

Ta có: \(A=1+5+5^2+...+5^{2019}\)

\(=\left(1+5+5^2\right)+\left(5^3+5^4+5^5\right)+...+\left(5^{2017}+5^{2018}+5^{2019}\right)\)

\(=31+5^3\cdot31+...+5^{2017}\cdot31\)

\(=31\left(1+5^3+...+5^{2017}\right)\)

\(=-31\cdot\left(1+5^3+...+5^{2017}\right)\cdot\left(-1\right)⋮-31\)(đpcm)