Question

S = 2 + 2² + 2³ + ...+ 2⁹⁹

chúng minh S ⋮ 5 và S ⋮10

Answer 1

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

\(=\left(2+2^2+2^3+2^4\right)+...+2^{95}\left(2+2^2+2^3+2^4\right)\)

\(=30\left(1+...+2^{95}\right)⋮10\)