\(A=5+5^2+5^3+........+5^8\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+......+\left(5^7+5^8\right)\)
\(A=5.\left(1+5\right)+5^3.\left(1+5\right)+...+5^7.\left(1+5\right)\)
\(A=5.6+5^3.6+......+5^7.6\)
\(A=6.\left(5+5^3+.....+5^7\right)\)
\(A=3.2.\left(5+5^3+....+5^7\right)\)
\(\Leftrightarrow A⋮2\)
mà \(A⋮5\)
\(\Rightarrow A⋮\left(2.5\right)\Leftrightarrow A⋮10\)
Vậy A là bội của 10.
b/ \(B=3+3^3+3^5+...+3^{39}\)
\(B=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+....+\left(3^{35}+3^{37}+3^{39}\right)\)
\(B=1.\left(3+3^3+3^5\right)+3^6.\left(3+3^3+3^5\right)+....+3^{34}.\left(3+3^3+3^5\right)\)
\(B=1.273+3^6.273+.....+3^{34}.273\)
\(B=273.\left(1+3^6+...+3^{34}\right)\)
\(\Rightarrow B⋮273\)
Vậy B là bội của 273
Nhớ k cho mình nhé! Thank you!!!
