Question

^{chứng minh rằng}

tổng A=2+2^2+2^3+2^4+...+2^12 chia hết cho 7

Answer 1

A = (2+2^2+2^3)+(2^4+2^5+2^6)+(2^7+2^8+2^9)+(2^10+2^11+2^12)

   = 2.(1+2+2^2)+2^4.(1+2+2^2)+2^7.(1+2+2^2)+2^10.(1+2+2^2)

   = 2.7+2^4.7+2^7.7+2^10.7

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

Tk mk nha

Answer 2

A = 2 + 2² + 2³ + 2⁴ + . . . + 2¹²

A = ( 2 + 2² + 2³ ) + . . . + ( 2¹⁰ + 2¹¹ + 2¹² )

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

A = 2 . 7 + 2⁴ . 7 + . . . + 2¹⁰ . 7

A = 7 . ( 2 + 2⁴ + . . . + 5¹⁰ ) \(⋮\)7

=> A \(⋮\)7