Question

[Nguyễn thị Ngà]

1.Cho tổng T=3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9

       Chứng minh T chia hết cho 13

Answer 1

[ST]

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

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

\(T=3.\left(1+3+3^2\right)+3^4.\left(1+3+3^2\right)+3^7.\left(1+3+3^2\right)\)

\(T=3.13+3^4.13+3^7.13\)

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