Question

Cho A=2+2^3+2^4+2^5+2^6+......+2^20     . Chứng tỏ      rằng A chia hết cho 3

 

Answer 1

Ta có:A=2+2^3+2^4+2^5+2^6+2^7......+2^19+2^20

A=(2+2^3)+(2^4+2^5)+(2^6+2^7)+.....+(2^19+2^20)

A=2(1+2)+2^4(1+2)+2^6(1+2)+......+2^19(1+2)

A=2.3+2^4.3+2^6.3+.......+2^19.3

A=3.(2+2^4+2^6+...+2^19)

Vì 3 chia hết cho => 3.(2+2^4+2^6+...+2^19)chia hết cho 3

Vậy A chia hết cho 3

Answer 2

vì 3 chia het cho 3.(2+2^4+......+2^19)

vay a chia het cho 3