Question

[Hưng....(NL) 《Grey Heffley 》]

A=2¹+2²+2³+...+2¹¹+2¹²

chứng minh A chia hết cho 3

Answer 1

[cat]

A=(2+2²)+(2³+2⁴)+...+(2¹¹+2¹²)

A=2(1+2)+2³(1+2)+...+2¹¹(1+2)

A=2.3+2³.3+...+2¹¹.3

Vì  3 chia hết cho 3

=>2.3+2³.3+...+2¹¹.3 chia hết cho 3

Vậy A chia hết cho 3

Answer 2

[Trieu van]

\(A=2^1+2^2+2^3+...+2^{11}+2^{12}\)

\(A=\left(2^1+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{11}+2^{12}\right)\)

\(A=\left(2^1+2^2\right)+2^2.\left(2^1+2^2\right)+...+2^{10}.\left(2^1+2^2\right)\)

VÌ \(\left(2^1+2^2\right)=6\)CHIA HẾT CHO 3

=>\(\left(2^1+2^2\right)+2^2.\left(2^1+2^2\right)+...+2^{10}.\left(2^1+2^2\right)\)CHIA HẾT CHO 3

=>\(A\)CHIA HẾT CHO 3