Question

Chứng minh rằng

2+2²+2³+2⁴+...+2³⁰ chia hết cho 7

mình đang cần gấp nha,thanks mn

Answer 1

Ta có : 2 + 2² + 2³ + ..... + 2³⁰ 

= (2 + 2² + 2³) + ..... + (2²⁸ + 2²⁹ + 2³⁰)

= 2.(1 + 2 + 2²) + ...... + 2²⁸(1 + 2 + 2²)

= 2.7 + ..... + 2²⁸.7

= 7(2 + ..... + 2²⁸) chia hết cho 7 

Answer 2

2+2²+2³+2⁴+...+2³⁰=(2+2²+2³)+(2⁴+2⁵+2⁶)+...+(2²⁸+2²⁹+2³⁰)

= 2(1+2+2²)+2⁴(1+2+2²)+...+2²⁸(1+2+2²)=

= (1+2+2²)(2+2⁴+...+2²⁸)=7.(2+2⁴+...+2²⁸)  => Chia hết cho 7

Answer 3

\(2+2^2+2^3+2^4+...+2^{28}+2^{29}+2^{30}\)

\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{28}+2^{29}+2^{30}\right)\)

\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{28}\left(1+2+2^2\right)\)

\(=2.7+2^4.7+...+2^{28}.7\)

\(=7\left(2+2^4+...+2^{28}\right)\) chia hết cho 7

Answer 4

sao cần gấp nhiều vậy bạn?