Question

[Tôi muốn mik giỏi toán]

Cho A= 2​^1  + 2^{2 +} 2³+.... +2​​ mũ ​​​​​​​​90( ko an duoc)

Chứng    to A chia het cho 7

Answer 1

[Nguyễn Huy Tú]

A = 21 + 22 + 23 + ... + 290

=> A = ( 21 + 22 + 23 ) + ... + ( 288 + 289 + 290 )

=> A = 2. ( 1 + 2 + 22 ) + ... + 288.( 1 + 2 + 22 )

=> A = 2 . 7 + ... + 288 . 7

=> A = ( 2 + ... + 288 ) . 7 \(⋮\)7

\(\Rightarrow A⋮7\)

Answer 2

[Lucy Heartfilia]

A = 2 + 2² + 2³ + ... + 2⁹⁰

A =  ( 2 + 2² + 2³ ) +... + ( 2⁸⁸ + 2⁸⁹ + 2⁹⁰ )

A = 2 . ( 1 + 2 + 4 ) + ... + 2⁸⁸ . ( 1 + 2 + 4 )

A = 2 . 7 + .. + 2⁸⁸ . 7

A = ( 2 + .. + 2⁸⁸ ) . 7 \(⋮\)7

Vậy A \(⋮\)7