Question

chứng minh q = 2+2 mũ 2 +2 mũ 3 ...+ 2 mũ 39 chia hết cho 13

Answer 1

\(Q=2+2^2+2^3+...+2^{99}\)

\(=\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{98}+2^{99}\right)\)

\(=6+2^2.\left(2+2^2\right)+...+2^{97}.\left(2+2^2\right)\)

\(=6+2^2.6+...+2^{97}.6\)

\(=6.\left(1+2^2+...+2^{97}\right)\)

Vì \(6⋮3\) nên \(6.\left(1+2^2+...+2^{97}\right)⋮3\)

Vậy \(Q⋮3\)

\(#WendyDang\)