Bài 9:
\(D=1+4+4^2+\cdots+4^{59}\)
\(=\left(1+4+4^2\right)+\left(4^3+4^4+4^5\right)+\cdots+\left(4^{57}+4^{58}+4^{59}\right)\)
\(=\left(1+4+4^2\right)+4^3\left(1+4+4^2\right)+\cdots+4^{57}\left(1+4+4^2\right)\)
\(=21\left(1+4^3+\cdots+4^{57}\right)\)
=>D⋮21
Bài 8:
a chia 36 dư 12
=>a=36k+12
=>a=4(9k+3)⋮4
a=36k+12
=36k+9+3
=9(4k+1)+3
=>a không chia hết cho 9
Bài 7:
a: \(A=2+2^2+\cdots+2^{20}\)
\(=2\left(1+2+\cdots+2^{19}\right)\) ⋮2
b: Ta có: \(A=2+2^2+\cdots+2^{20}\)
\(=\left(2+2^2\right)+\left(2^3+2^4\right)+\cdots+\left(2^{19}+2^{20}\right)\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+\cdots+2^{19}\left(1+2\right)\)
\(=3\left(2+2^3+\cdots+2^{19}\right)\) ⋮3
c: \(A=2+2^2+\cdots+2^{20}\)
\(=\left(2+2^2+2^3+2^4\right)+\left(2^5+2^6+2^7+2^8\right)+\cdots+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\)
\(=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+\cdots+2^{17}\left(1+2+2^2+2^3\right)\)
\(=15\left(2+2^5+\cdots+2^{17}\right)\)
=>A⋮5
