Question

C/M a= 2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2¹⁰+2¹¹+2¹²  chia hết cho 7

Answer 1

Ta có:

A=2+2²+2³+2⁴+2⁵+2⁶+2⁷+2⁸+2⁹+2¹⁰+2¹¹+2¹²

  =(2+2²+2³)+(2⁴+2⁵+2⁶)+(2⁷+2⁸+2⁹)+(2¹⁰+2¹¹+2¹²)

  =2.(1+2+4)+2⁴.(1+2+4)+2⁷.(1+2+4)+2¹⁰.(1+2+4)

  =(2+2⁴+2⁷+2¹⁰).7

=>A chia hết cho 7

Answer 2

Đề đúng là \(a=2+2^2+2^3+.......+2^{10}+2^{11}+2^{12}\)chia hết cho 7

\(a=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+2^7\left(1+2+2^2\right)+2^{10}\left(1+2+2^2\right)\)

\(a=2.7+2^4.7+2^7.7+2^{10}.7\)

\(a=7\left(2+2^4+2^7+2^{10}\right)\) chia hết cho 7 

Vậy a chia hết cho 7