Question

chứng tỏ rằng a) A=2ᒾ + 2³ +2⁴ + .....+2⁹⁹ chia hết cho 3 

Giúp mik nha

Answer 1

Ta có:

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

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

\(A=12+2^2.\left(2^2+2^3\right)+...+2^{96}.\left(2^2+2^3\right)\)

\(A=12+2^2.12+...+2^{96}.12\)

\(A=12.\left(1+2^2+...+2^{96}\right)\)

Vì \(12⋮3\) nên \(12.\left(1+2^2+...+2^{96}\right)⋮3\)

Vậy \(A⋮3\)