Question

chứng minh rằng

1+2¹+2²⁺2³+2⁴+2⁵+2⁶+2⁷chia hết cho3

 

Answer 1

ta có:

1+2¹+2²+2³+2⁴+2⁵+2⁶+2⁷

=1+2¹+(2²+2³)+(2⁴+2⁵)+(2⁶+2⁷)

=(1+2)+2².(1+2)+2⁴.(1+2)+2⁶.(1+2)

=(1+2).(1+2²+2⁴+2⁶)

=3.(1+2²+2⁴+2⁶) chia hết cho 3

=>đpcm

Answer 2

=\(\left(1+2^1\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)

\(=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)

\(=3+2^2.3+2^4.3+2^6.3\)

\(=3\left(1+2^2+2^4+2^6\right)\) CHIA HẾT CHO 3

Answer 3

gọi C là tên biểu thức trên.ta có :

C = 1+2¹+2²⁺2³+2⁴+2⁵+2⁶+2⁷

C = ( 1 + 2¹ ) + ( 2² + 2³ ) + ( 2⁴ + 2⁵ ) + ( 2⁶ + 2⁷ )

C = 3 + 2² . ( 1 + 2¹ ) + 2⁴ . ( 1 + 2¹ ) + 2⁶ . ( 1 + 2¹ )

C = 3 + 2² . 3 + 2⁴ . 3 + 2⁶ . 3

C = 3 . ( 1 + 2² + 2⁴ + 2⁶ ) chia hết cho 3