Question

Cho A = 2^1+2^2+2^3+...+2^8+2^9

Chứng minh A chia hết cho 7!!

Answer 1

A=  \(\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+\left(2^7+2^8+2^9\right)\)

\(=2.7+2^4.7+2^7.7\)

\(=7.\left(2+2^4+2^7\right)\)

Chia het cho 7 

Answer 2

2¹+2²+2³+........+2⁹

=(2¹+2²+2³)+(2⁴+2⁵+2⁶)+(2⁷+2⁸+2⁹)

=2.(1+2+2²)+2⁴.(1+2+2²)+2⁷.(1+2+2²) chia het cho 7

=>dpcm