Question

Cho M=2+2^2+2^3+...+2^20

Chứng tỏ rằng M chia hết cho 5.

giúp!

Answer 1

\(M=\left(2+2^2+2^3+2^4\right)+...+\left(2^{17}+2^{18}+2^{19}+2^{20}\right)\\ M=2\left(1+2+2^2+2^3\right)+...+2^{17}\left(1+2+2^2+2^3\right)\\ M=\left(1+2+2^2+2^3\right)\left(2+...+2^{17}\right)\\ M=15\left(2+...+2^{17}\right)⋮5\)

Answer 2

\(M=\left(2+2^2+2^3+2^4\right)+...+2^{16}\left(2+2^2+2^3+2^4\right)\)

\(=30\left(1+...+2^{16}\right)⋮5\)

Answer 3

=(2+2^2+2^3+2^4)+....+(2^17+2^18+2^19+2^20)

=30.1+...+30.(2^16+2^16+2^16+2^16)

=30.(1+...)

vì 30 chia hết cho 5 suy ra M chia hết cho 5