Question

cho A=2 + 2^2+2^3+2^4+ ...+2^99+2^100

Chứng minh rằng A chia hết cho 31

giúp mk vs

Answer 1

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

\(\Rightarrow A=\left(2+2^2+2^3+2^4+2^5\right)+.......+\left(2^{96}+2^{97}+2^{98}+2^{99}+2^{100}\right)\)

\(\Rightarrow1.\left(2+2^2+2^3+2^4+2^5\right)+.......+1.\left(2+2^2+2^3+2^4+2^5\right)\)

\(\Rightarrow1.62+......+1.62\)

Mà 62 \(⋮\)31 => A \(⋮\)31