Question

chứng minh 5+5^2+5^3+5^4+5^5+5^6+5^7+5^8 chia hết cho 30

Answer 1

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

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

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

\(=30.\left(1+5^2+...+5^6\right)\) chia hết cho 30 (đpcm).

Answer 2

 5+5^2+5^3+5^4+5^5+5^6+5^7+5^8

  = (5+5^2)+(5^3+5^4)+(5^5+5^6)+(5^7+5^8)

  = (5+5^2)+5^2.(5+5^2)+5^4.(5+5^2)+5^6.(5+5^2)

  = (5+5^2). (1+5^2+5^4+5^6) = 30. (1+5^2+5^4+5^6) chia hết cho 30