Question

A=2+2^2+2^3+2^4+....+2^100 . chứng minh A chia hết cho 3

Answer 1

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

\(=3\left(2+...+2^{99}\right)⋮3\)

Answer 2

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

\(=>A=3.\left(2+2^3+....+2^{99}\right)⋮3\)