Question

Cho M=2+2^2+2^3+2^4+...+2^20

Chứng tỏ rằng M chia hết cho 5

giúp với!

Answer 1

\(M=2\left(1+2+2^2+2^3\right)+2^5\left(1+2+2^2+2^3\right)+...+2^{17}.\left(1+2+2^2+2^3\right)\)

\(=2.15+2^5.15+...+2^{17}.15=5.3\left(2+2^5+...+2^{17}\right)⋮5\)

Answer 2

\(M=2+2^2+2^3+2^4+...+2^{19}+2^{20}\)

\(=\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{19}\left(2+2^2\right)\)

\(=5+5.2^2+...+5.2^{19}\)

\(=5\left(1+2^2+...+2^{19}\right)\) ⋮5