Question

Chứng tỏ rằng A chia hết cho 6 với A=2+2²+2³+2⁴+....+2¹⁰⁰

Answer 1

\(A=2+2^2+2^3+2^4+...+2^{99}+2^{100}\\ \Rightarrow A=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{99}+2^{100}\right)\\ \Rightarrow A=\left(2+2^2\right)+2^2\left(2+2^2\right)+...+2^{98}\left(2+2^2\right)\\ \Rightarrow A=\left(2+2^2\right)\left(1+2^2+...+2^{98}\right)\\ \Rightarrow A=6\left(1+2^2+...+2^{98}\right)⋮6\)