Question

A=2^1+2^2+...+2^59+2^60

Chứng minh A chia hết cho 7

Answer 1

A=2^1+2^2+...+2^60=(2^1+2^2+2^3)+...+(2^58+2^59+2^60)=2^1.(1+2+2^2)+2^4.(1+2+2^2)+...+2^58.(1+2+2^2)=2^1.7+2^4.7+...+2^58.7

  =7.(2^1+2^4+...+2^58) chia hết cho 7 (đpcm)

Answer 2

A = 2 ^ 1 + 2 ^ 2 + ... + 2 ^ 59 + 2 ^ 60

A = ( 2 ^ 1 + 2 ^ 2 + 2 ^ 3 ) + ... + ( 2 ^ 58 + 2 ^ 59 + 2 ^ 60 )

A = ( 2 ^ 1 + 2 ^ 2 + 2 ^ 3 ) + ... + ( 2 ^ 1 + 2 ^ 2 + 2 ^ 3 ) . 2 ⁵⁷

A = 14 + ... + 14 . 2 ⁵⁷

A = 14 ( 1 + ... + 2 ⁵⁷ )

Vì 14 chi hết cho 7

=> A chia hết cho  7

Answer 3

A=(2¹+2²+2³)+(2⁴+2⁵+2⁶)+...+(2⁵⁸+2⁵⁹+2⁶⁰)

=>A=2.(1+2+2²)+2⁴.(1+2+2²)+.....+2⁵⁸.(1+2+2²)

=>A=2.7+2⁴.7+...+2⁵⁸.7

=>A=7.(2+2⁴+...+2⁵⁸) chia hết  cho 7

=>A chia hết cho 7 (đpcm)

Answer 4

Ta có : A = ( 2¹ + 2² + 2³ ) + ( 2⁴  + 2⁵ + 2⁶ ) + ..... + ( 2⁵⁸ + 2⁵⁹ + 2⁶⁰ )

= 2( 1 + 2 + 2² ) + 2⁴( 1 + 2 + 2² ) + .... + 2⁵⁸ ( 1 + 2 + 2² )

= 2.7 + 2⁴.7 + .... + 2⁵⁸ .7

= 7(2 + 2⁴ + ... + 2⁵⁸ ) chia hết cho 7

=> A chia hết cho 7