Question

[Tăng Thị Cẩm Tú]

cho M= 1+3+3^2+3^3+......+3^118+3^119

cmr:  M chia hết cho 13

Answer 1

[Thieu Gia Ho Hoang]

bai toan nay kho quá

Answer 2

[Minh Hiền]

\(M=\left(1+3+3^2\right)+\left(3^3+3^4+3^5\right)+...+\left(3^{117}+3^{118}+3^{119}\right)\)

\(=13+3^3.\left(1+3+3^2\right)+...+3^{117}.\left(1+3+3^2\right)\)

\(=13+3^3.13+...+3^{117}.13\)

\(=13.\left(1+3^3+...+3^{117}\right)\text{chia hết cho 13}\)

=> M chia hết cho 13 (Đpcm).