Question

Cho A=2+2²+2³+2⁴+...+2^{60                Chứng tỏ rằng A chia hết cho 3}

Answer 1

A= (2+2^2)+ (2^3+2^4)+.....+(2^59+2^60)

= 2.(1+2)+ 2^3.(1+2)+...+ 2^59.(1+2)

= 3.(2+2^3+...+2^59) luôn chia hết cho 3

Vậy A chia hết cho 3

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Answer 2

Huyền nhi làm thiếu

Answer 3

còn 

Answer 4

A=2+22+23+....+260

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

A=2.3+23.3+....+259.3 chia hết cho 3

Answer 5

A=2+2²+2³+2⁴+...+2⁶⁰

A=(2+2²)+(2³+2⁴)+...+(2⁵⁹+2⁶⁰)

A=2.(1+2)+2³.(1+2)+...+2⁵⁹.(1+2)

A=2.3+2³.3+...+2⁵⁹.3

A=3.(2+2³+...+2⁵⁹) \(⋮\) 3

Vậy A \(⋮\) 3

# LGC #

Answer 6

A = \(\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\)

= \(2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)

= 3\(\left(2+2^3+...+2^{59}\right)\)\(⋮\) 3

\(\Rightarrow A⋮3\)