Question

A = 1 + 2^1+2^2+2^3 +...........+2^10+2^11 . Cmr A chia hết cho 3

Answer 1

A = ( 1 + 2^1 ) + ( 2^2 + 2^3 ) + ... + ( 2^10 + 2^11 )

A = 3 . 1 + 3 . 4 + ... + 3 . 1024

A = 3 ( 1 + 4 + ... + 1024 )

=> A chia hết cho 3 

Answer 2

\(A=\left(1+2\right)+\left(2^2+2^3\right)+...........+\left(2^{10}+2^{11}\right)\)

\(=3+2^2.3+.............+2^{10}.3\)

\(=\left(1+2^2+........+2^{10}\right).3\) chia hết cho 3

Vậy A chia hết cho 3