Question

cho a = 2 + 2 mũ 2 + 2 mũ 3 + 2 mũ 4 ....... 2 mũ 100 chứng minh rằng a chia hết cho 3 

Answer 1

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

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

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

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