Question

cho S = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 . Chứng tổ rằng S chia hết cho 3

 

Answer 1

\(S=1+2+2^2+...+2^7\)

\(=\left(1+2\right)+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)

\(=\left(1+2\right)+2^2\left(1+2\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)

\(=3\left(1+2^2+2^4+2^6\right)⋮3\)

Answer 2

S=(1+2)+(2^2+2^3)+...+(2^6+2^7)

S=3+3(2^2)+...+3(2^6)

S=3(2^0+2^2+...+2^6)

suy ra S chia hết cho 3