Question

Answer 1

\(1+5+5^2+...+5^{12}\)

\(=1+5\left(1+5+5^2\right)+...+5^{10}\left(1+5+5^2\right)\)

\(=1+5.31+...+5^{10}.31=1+31\left(5+...+5^{10}\right)\)

=> Chia 31 dư 1

Answer 2

\(1+5+5^2+...+5^{12}\\ =1+\left(5+5^2+5^3\right)+\left(5^4+5^5+5^6\right)+...+\left(5^{10}+5^{11}+5^{12}\right)\\ =1+5\left(1+5+5^2\right)+5^4\left(1+5+5^2\right)+...+5^{10}\left(1+5+5^2\right)\\ =1+\left(1+5+5^2\right)\left(5+5^4+...+5^{10}\right)\\ =1+31\left(5+5^4+...+5^{10}\right)\)

Vậy tổng chia 31 dư 1