b: \(B=5+5^2+5^3+5^4+...+5^{99}+5^{100}\)
\(=5\left(1+5\right)+...+5^{99}\left(1+5\right)\)
\(=6\cdot\left(5+...+5^{99}\right)⋮6\)
a) \(A=1+3+3^2+...+3^{99}\)
\(=\left(1+3+3^2+3^3\right)+3^4\left(1+3+3^2+3^3\right)+...+3^{96}\left(1+3+3^2+3^3\right)\)
\(=40+3^4.40+...+3^{96}.40=40\left(1+3^4+...+3^{96}\right)⋮40\)