Question

chứng minh rằng A=2+2²+2³+2⁴+...+2⁶⁰ chia hết cho 3,7 ,15

Answer 1

A=(2+2²)+(2³+2⁴⁾+......+(2⁵⁹+2⁶⁰)

A=2(1+2)+2³(1+2)+.....+2⁵⁹(1+2)

A=2.3+2³.3+.......+2⁵⁹.3

A=3.(2+2³+......+2⁵⁹)

Vậy A chia hết cho 3

 

A=(2+2²+2³)+(2⁴+2⁵+2⁶)+.......+(2⁵⁸+2⁵⁹+2⁶⁰)

A=2(1+2+4)+2⁴(1+2+4)+.........+2⁵⁸(1+2+4)

A=2.7+2⁴.7+........2⁵⁸.7

A=7.(2+2⁴+.............+2⁵⁸)

Vậy A chia hết cho 7

 

 

A=(2+2²+2³+2⁴)+..............+(2⁵⁷+2⁵⁸+2⁵⁹+2⁶⁰)

A=2(1+2+4+8)+.............+2⁵⁷(1+2+4+8)

A=2.15+..........+2⁵⁷.15

A=15(2+...........+2⁵⁷)

Vậy A chia hết cho 15