Question

Chứng minh : B=1+2+2^2+2^3+...+2^11 chia hết cho 9

 

Answer 1

Ta có 

\(B=\left(1+2^3\right)+2^2\left(1+2^3\right)+......+2^8\left(1+2^3\right)=9\left(1+2^2+....+2^8\right)\) Chia hết cho 9

(đpcm)

Answer 2

\( B=1+2+2^2+2^3+...+2^{11}\)

\(\Leftrightarrow B=\left(1+2^3\right)+2^2\left(1+2^3\right)+2^3\left(1+2^3\right)+...+2^8\left(1+2^3\right)\)

\(\Leftrightarrow B=9+2^2.9+2^3.9+...+2^8.9\)

\(\Leftrightarrow B=9\left(1+2^2+2^3+...+2^8\right)\)

Vậy \(B⋮9\left(ĐPCM\right)\)