Question

a) ChoA=2+2^2+2^3+2^4+....+2^99+2^100

Hỏi A có chia hết cho 3, cho 7 không? Vì sao?

b) B=3+3^3+3^5+....+3^1991

Chứng minh B chia hết cho 13, 41

Answer 1

a: \(A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{99}\left(1+2\right)\)

=3(2+2^3+...+2^99) chia hết cho 3

b: Sửa đề: \(B=3+3^2+3^3+...+3^{1990}+3^{1991}+3^{1992}\)

\(=3\left(1+3+3^2\right)+...+3^{1990}\left(1+3+3^2\right)\)

\(=13\left(3+...+3^{1990}\right)⋮13\)