\(2^2+2^3+2^4+2^5+...+2^{99}=2^2\left(1+2\right)+2^4\left(1+2\right)+...+2^{98}\left(1+2\right)=3.2^2+3.2^4+...+3.2^{98}=3\left(2^2+2^4+...+2^{98}\right)⋮3\)
\(B=2^2+2^3+...+2^{99}\)
\(B=\left(2^2+2^3\right)+...+\left(2^4+2^5\right)+...+\left(2^{98}+2^{99}\right)\)
\(B=3.2^2+3.2^4+...+3.2^{98}\)
\(B=3.\left(2^2+2^4+...+2^{98}\right)\)
\(\Rightarrow B⋮3\)
Ta có: \(B=2^2+2^3+2^4+2^5+...+2^{98}+2^{99}\)
\(=2^2\left(1+2\right)+2^4\left(1+2\right)+...+2^{98}\left(1+2\right)\)
\(=3\cdot\left(2^2+2^4+...+2^{98}\right)⋮3\)