Question

chứng minh:b=2 mũ 1+2 mũ 2+2 mũ 3+2 mũ 4+...+2 mũ 200+2 mũ 201 

b chia hết cho 7

Answer 1

\(B=2^1+2^2+2^3+2^4+...+2^{200}+2^{201}\)\(\Rightarrow B=2\left(1+2^1+2^2\right)+2^4\left(1+2^1+2^2\right)+...+2^{199}\left(1+2^1+2^2\right)\)

\(\Rightarrow B=2.7+2^4.7+...+2^{199}.7\)

\(\Rightarrow B=7.\left(2+2^4+...+2^{199}\right)⋮7\Rightarrow dpcm\)