Question

[LÊ DƯƠNG QUỲNH TRÂM]

B=3+3^2+3^3+...+3^118+3^119+3^120

CHỨNG MINH RẰNG B CHIA HẾT CHO 13

Answer 1

[GV Nguyễn Trần Thành Đạt]

\(B=3+3^2+3^3+...+3^{118}+3^{119}+3^{120}\\ =\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{118}+3^{119}+3^{120}\right)\\ =3.\left(1+3+3^2\right)+3^4.\left(1+3+3^2\right)+...+3^{118}\left(1+3+3^2\right)\\ =\left(3+3^4+...+3^{118}\right).\left(1+3+3^2\right)\\ =\left(3+3^4+...+3^{118}\right).13⋮13\left(ĐPCM\right)\)

Answer 2

[LÊ DƯƠNG QUỲNH TRÂM]

thanks