Question

Tìm số dư

(1+5+5²+5^3+.........+5¹⁹⁹⁵)chia hết cho 31

(1+2+2²+.........+2¹⁰¹⁾chia hết cho 15

Answer 1

Đề phải là chứng minh nhé bạn:

\(1+5+5^2+...+5^{1995}\)

\(=\left(1+5+5^2\right)+...+\left(5^{1993}+5^{1994}+5^{1995}\right)\)

\(=\left(1+5+5^2\right)+...+5^{1993}.\left(1+5+5^2\right)\)

\(=31+...+5^{1993}.31\)

\(=31.\left(1+...+5^{1993}\right)⋮31\left(đpcm\right)\)

\(1+2+2^2+...+2^{101}\)

\(=\left(1+2+2^2+2^3\right)+...+\left(2^{98}+2^{99}+2^{100}+2^{101}\right)\)

\(=\left(1+2+2^2+2^3\right)+...+2^{98}.\left(1+2+2^2+2^3\right)\)

\(=15+...+2^{98}.15\)

\(=15.\left(1+...+2^{98}\right)⋮15\left(đpcm\right)\)