Ta có : A=22+24+26+...+220
=(22+24)+(26+28)+...+(218+220)
=22(1+22)+26(1+22)+...+218(1+22)
=22.5+26.5+...+218.5 chia hết cho 5
Vậy A chia hết cho 5.
\(A=2^2+2^4+2^6..+2^{18}+2^{20}\)
\(\Leftrightarrow A=\left(2^2+2^4\right)+\left(2^6+2^8\right)+...+\left(2^{18}+2^{20}\right)\)
\(\Leftrightarrow A=20+2^4.\left(2^2+2^4\right)+...+2^{16}.\left(2^2+2^4\right)\)
\(\Leftrightarrow A=20+2^4.20+..+2^{16}.20\)
\(\Leftrightarrow A=20\left(1+2^4+..+2^{16}\right)\)
Vì \(20⋮5\)
\(\Rightarrow A=20\left(1+2^4+..+2^{16}\right)⋮5\)
Vậy \(A⋮5\)
hok tốt!!
\(A=2^2+2^4+2^6+2^8+....+2^{18}+2^{20}\)
\(A=\left(2^2+2^4\right)+\left(2^6+2^8\right)+....+\left(2^{18}+2^{20}\right)\)
\(A=2^2\left(1+2^2\right)+2^6\left(1+2^2\right)+....+2^{18}\left(1+2^2\right)\)
\(A=2^2\cdot5+2^6\cdot5+...+2^{18}\cdot5\)
\(A=5\left(2^2+2^6+...+2^{18}\right)\)
=> A chia hết cho 5
\(A=2^2+2^4+2^6+2^8+...+2^{18}+2^{20}\)
\(=\left(2^2+2^4\right)+\left(2^6+2^8\right)+...+\left(2^{18}+2^{20}\right)\)
\(=2^2.\left(1+2^2\right)+2^6.\left(1+2^2\right)+...+2^{18}.\left(1+2^2\right)\)
\(=2^2.5+2^6.5+...+2^{18}.5\)
Vậy \(A\)chia hết cho \(5\)