Question

Cho A =2⁰+2¹+2²+2³+.....+2²⁰¹⁶

Tìm số dư khi đem A chia cho 7

Answer 1

Ta Có :

    A =2⁰+2¹+2²+2³+.....+2²⁰¹⁶

=>A = 2⁰(1+2+4) + 2³(1+2+4) + ...... + 2²⁰¹⁴(1+2+4)

=>A = 1.7 + 2³.7 + ....... +2²⁰¹⁴ . 7

=>A = 7.(1+2³+......+2²⁰¹⁴)

=> A chia hết cho 7 (ĐPCM)

Đúng thì cho tích nha bạn !

Answer 2

Số dư là 0

Answer 3

\(A=2^0+2^1+2^2+2^3+...+2^{2016}\)

\(A=1+\left(2^1+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{2014}+2^{2015}+2^{2016}\right)\)

\(A=1+2^1.\left(1+2+2^2\right)+2^4.\left(1+2+2^2\right)+...+2^{2014}.\left(1+2+2^2\right)\)

\(A=1+2^1.7+2^4.7+...+2^{2014}.7\)

\(A=1+7.\left(2^1+2^4+...+2^{2014}\right)\)

\(\Rightarrow\) A  chia cho 7 dư 1.