Question

Chứng minh. A=2+2^2+2^3+2^4...+2^60 chia hết cho 3

Answer 1

\(A=2+2^2+2^3+2^4+...+2^{60}\\ =\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\\ =\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{58}\left(2+2^2\right)\\ =\left(2+2^2\right).\left(1+2^2+...+2^{58}\right)\\ =6.\left(1+2^2+...+2^{58}\right)⋮3\left(Vì:6⋮3\right)\)

Answer 2

A = 2 + 2² + 2³ + ... + 2⁵⁹ + 2⁶⁰

= (2 + 2²) + (2³ + 2⁴) + ... + (2⁵⁹ + 2⁶⁰)

= 2(1 + 2) + 2³(1 + 2) + ... + 2⁵⁹(1 + 2)

= 2.3 + 2³.3 + ... + 2⁵⁹.3

= 3(2 + 2³ + ... + 2⁵⁹) ⋮ 3

Answer 3

Ta có: �=(2+22)+(23+24)+...+(259+260)A=(2+22)+(23+24)+...+(259+260)

=2.(1+2)+23.(1+2)+...+259.(1+2)=2.(1+2)+23.(1+2)+...+259.(1+2)

=2.3+23.3+...+259.3=2.3+23.3+...+259.3

=3.(2+23+...+259)=3.(2+23+...+259)chia hết cho 3

=> A chia hết cho 3 (Đpcm).