Question

cho A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10 chung to A chia het cho 3

Answer 1

A = 2 + 2² + 2³ + 2⁴ + ........+ 2⁹ + 2¹⁰

  = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ....... + ( 2⁹ + 2¹⁰ )

  = 2 x ( 1 + 2 ) + 2³ x ( 1 + 2 ) + ...... + 2⁹ x ( 1 + 2 )

 = 2 x 3 + 2³ x 3 + .......... + 2⁹ x 3

 = 3 x ( 2 + 2³ + ...... + 2⁹ )

= > vì 3 chia hết cho 3 nên A chia hết cho 3

 

Answer 2

A = 2 + 2² + ... + 2¹⁰

   = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ... + ( 2⁹ + 2¹⁰ )

   = 2.(1+2) + 2³.(1+2) + ... + 2⁹.(1+2)

   = 2.3 + 2³.3 + ... + 2⁹.3

   = 3.(2+2³+...+2⁹) chia hết cho 3

Answer 3

A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9+2^10

A=(2+2^2)+2^2.(2+2^2)+2^4.(2+2^2)+2^6.(2+2^2)+2^8.(2+2^2)

A=6+2^2.6+2^4.6+2^6.+2^8

A=(1+2^2+2^4+2^6+2^8).6

=> A chia hết cho 3

Answer 4

A = 2 + 2² + ... + 2¹⁰

   = ( 2 + 2² ) + ( 2³ + 2⁴ ) + ... + ( 2⁹ + 2¹⁰ )

   = 2.(1+2) + 2³.(1+2) + ... + 2⁹.(1+2)

   = 2.3 + 2³.3 + ... + 2⁹.3

   = 3.(2+2³+...+2⁹) chia hết cho 3