Question

Chứng tỏ \(A=5+5^2+5^3+...+5^8\)chia hết cho 30

Answer 1

\(A=5+5^2+5^3+5^4+..+5^7+5^8\)

\(A=\left(5+5^2\right)+5^2\left(5+5^2\right)+...+5^6\left(5^7+5^8\right)\)

\(A=30+5^2.30+...+5^6.30\)

\(A=30.\left(1+5^2+...+5^6\right)⋮30\)

\(\Rightarrow\) đpcm

Answer 2

\(A=5+5^2+5^3+...+5^8\\ A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^7+5^8\right)\)

\(A=30+5^2\left(5+5^2\right)+5^4\left(5+5^2\right)+...+5^6\left(5+5^2\right)\\ A=30+5^2.30+5^4.30+...+5^6.30\)

\(A=30\left(1+5^2+5^4+...+5^6\right)\\ \Rightarrow A⋮30\)