Question

cho A= 2 + 2^2+2^3+ .......2^12. chứng tỏ rằng A: 7

làm nhanh mình tick cho

Answer 1

a=(2+1+4).2³x........x2¹² 

^a=7x(2³x........x2¹² 

suy rA     :A CHIA HẾT CHO 7

Answer 2

=(2+2^2+2^3) + (2^4+2^5+2^6)....+(2^10+2^11+2^12)

= 14              + 2^3.14            ...........+  2^9 .14

=14. (1+2^3+2^9) :7

Answer 3

\(A=2+2^2+2^3+...+2^{12}\)

\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+\left(2^7+2^8+2^9\right)+\left(2^{10}+2^{11}+2^{12}\right)\)

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

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

\(A=7.\left(2+2^4+2^7+2^{10}\right)\)\(⋮\)\(7\)

\(\Rightarrow\)\(A⋮7\)

Answer 4

A = 2 + 2^2 + ........ + 2^12

   = 2 * ( 1 + 2 + 2^2 ) +2^4* ( 1 + 2 + 2^2) +......... + 2^10*(1 + 2 + 2^2)

   = 2 * 7 + 2^4 * 7 +.....................+ 2^10 * 7

   = ( 2 + 2^4 + ...+2^10)*7 chia hết cho 7

=> A chia hết cho 7

Answer 5

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

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

A = 2 . ( 1 + 2 + 2² ) + 2⁴ . ( 1 + 2 + 2² ) + 2⁷ ( 1 + 2 + 2² ) + 2¹⁰ . ( 1 + 2 + 2² )

A = (1 + 2 + 2² ) . ( 2 + 2⁴ + 2⁷ + 2¹⁰ )

A = 7 . ( 2 + 2⁴ + 2⁷ + 2¹⁰ ) \(⋮\)7

Vậy A \(⋮\)7