Ta có :
\(5+5^2+5^3+5^4+....+5^8\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^7+5^8\right)\)
\(=30+30.5^2+...+30.5^6\)
\(=30.\left(1+5^2+...+5^6\right)\)
\(=3.10.\left(1+5^2+...+5^6\right)⋮3\)
Vậy \(5+5^2+5^3+5^4+...+5^8\)chia hết cho 3 .
Học tốt
Bài làm :
Ta có :
\(5+5^2+5^3+5^4+5^5+5^6+5 ^7+5^8\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+\left(5^5+5^6\right)+\left(5^7+5^8\right)\)
\(=5\left(1+5\right)+5^3\left(1+5\right)+5^5\left(1+5\right)+5^7\left(1+5\right)\)
\(=\left(1+5\right)\left(5+5^3+5^5+5^7\right)\)
\(=6.\left(5+5^3+5^5+5^7\right)\)
Vì 6 chia hết cho 3
\(\Rightarrow6.\left(5+5^3+5^5+5^7\right)⋮3\)
=> Điều phải chứng minh
5 + 52 + 53 + 54 + ... + 58
= ( 5 + 52 ) + ( 53 + 54 ) + ... + ( 57 + 58 )
= 5( 1 + 5 ) + 53( 1 + 5 ) + ... + 57( 1 + 5 )
= 5.6 + 53.6 + ... + 57.6
= 6( 5 + 53 + ... + 57 )
Vì 6 chia hết cho 3 => 6( 5 + 53 + ... + 57 ) chia hết cho 3
=> đpcm
