Chứng minh rằng S=3+3^2+3^3+...+3^9 chia hết cho -39

* Hướng dẫn giải

$\begin{array}{l}S=3+3^2+3^3+3^4+3^5+3^6+3^7+3^8+3^9\\ =\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+\left(3^7+3^8+3^9\right)\\ =39+3^3.39+3^6.39\\ =39.\left(1+3^3+3^6\right)⋮\left(-39\right)\end{array}$

Vậy S chia hết cho -39