Question

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

Answer 1

\(A=2+2^2+2^3+2^4+...+2^{99}+2^{100}\)

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

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

Answer 2

\(A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{99}+2^{100}\right)\\ A=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{99}\left(1+2\right)\\ A=\left(1+2\right)\left(2+2^3+...+2^{99}\right)=3\left(2+2^3+...+2^{99}\right)⋮3\)