Ta có A = \(5+5^2+5^3+...+5^8\)
= \(\left(5+5^2\right)+\left(5^3+5^4\right)+....+\left(5^7+5^8\right)\)
= 30 + \(5^2\left(5+5^2\right)+....+5^6\left(5+5^2\right)\)
= \(30+5^2.30+5^3.30+...+5^6.30\)
= \(30\left(1+5^2+5^3+5^4+5^5+5^6\right)\) chia hết cho 30
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+\left(5^5+5^6\right)+\left(5^7+5^8\right)\)
\(=1\left(5+25\right)+5^2\left(5+25\right)+5^4\left(5+25\right)+5^6\left(5+25\right)\)
\(=1.30+5^2.30+5^4.30+5^6.30\)
\(=30\left(1+5^2+5^4+5^6\right)⋮30\) (đpcm)
\(A = 5 + 5^2 + 5^3 + ...+ 5^8 = (5 + 5^2) + (5^3 + 5^4) + ... + (5^7 + 5^8)\\ = 5(5 + 1) + 5^3 (1+5) + ... + 5^7(1+5) = 5.6 + 5^3.6 + ... + 5^7.6\\\)
\(= 6(5 + 5^3 + ... + 5^7)\)⋮6 (1)
\(A = 5 + 5^2 + 5^3 + ... + 5^8 = 5(1 + 5 + 5^2 + ... + 5^7)\)⋮5(2)
(1)(2) suy ra điều phải chứng minh
B = 5 + 52 + 53 + 54 + ... + 58
B = (5 + 52) + (53 + 54) + ... + (57+58)
B = 30 + 52 (5+52) + ... + 56 (5+52)
B = 30 + 52 . 30 + ... + 56 . 30
B = (1 + 52 + ... + 56) . 30 ⋮ 30
\(A=5+5^2+5^3+...+5^8\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^7+5^8\right)\)
\(A=30+5^2\left(5+5^2\right)+5^4\left(5+5^2\right)+5^6\left(5+5^2\right)\)
\(A=30+30.5^2+30.5^4+30.5^6\)
\(A=30\left(1+5^2+5^4+5^6\right)\)
\(\Rightarrow A⋮30\left(đpcm\right)\)
Ta có A = 5+52+53+...+585+52+53+...+58
= (5+52)+(53+54)+....+(57+58)(5+52)+(53+54)+....+(57+58)
= 30 + 52(5+52)+....+56(5+52)52(5+52)+....+56(5+52)
= 30+52.30+53.30+...+56.3030+52.30+53.30+...+56.30
= 30(1+52+53+54+55+56)30(1+52+53+54+55+56) chia hết cho 30
