Question

chung minh rang tong 3+3mu2+3mu3+3mu4+3mu5+3mu6+3mu7+3mu8+3mu9 chia het cho13

 

Answer 1

Rút gọn đc

3^10 - 3 = 3(3^9  - 1) = 3.(19683-1) = 3.1514.13 chia hết cho 13 

Answer 2

Ta có: \(3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9\)

\(=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+\left(3^7+3^8+3^9\right)\)

\(=3\left(1+3+9\right)+3^4\left(1+3+9\right)+3^7\left(1+3+9\right)\)

\(=\left(3+3^4+3^7\right).13\)chia hết cho 13