Question

[SHIBUKI RAN]

Chung minh:A=2+2²+2³+2⁴.....+2⁶⁰ chia hêt cho 3

Answer 1

[My Love bost toán]

A=2+2^2+2^3+2^4+...+2^60

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

A=6+2^2.(2+2^2)+...+2^58.(2+2^2)

A=6+2^2.6+....+2^58.6

A=6.(1+2^2+...+2^58)\(⋮\)6

=>A\(⋮\)6

vì A \(⋮\)6=>A\(⋮\)3=>ĐPCM

Answer 2

[Trần Thanh Phương]

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

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

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

\(A=2\cdot3+2^3\cdot3+...+2^{59}\cdot3\)

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