Question

Cho A = 2+2²+2³+2⁴+...+2^{20 Chứng tỏ A chia hết cho 3}

Answer 1

Ta có :

\(A=2+2^2+.....+2^{20}\)

\(\Rightarrow A=2\left(1+2\right)+....+2^{19}\left(1+2\right)\)

\(\Rightarrow A=2.3+....+2^{19}.3\)

=> A chia hết cho 3

Answer 2

Ta có :

A=2+2²⁺....+2²⁰

A=2\(\left(1+2\right)\)+2²\(\left(1+2\right)\)....+2¹⁹\(\left(1+2\right)\)

A=2.3+2².3+......+2¹⁹.3

A=\(\left(2+2^2+......+2^{19}\right)\).3

A chia hết cho 3