Question

Cho A=4+4²⁺4³+4⁴+.......+4⁹⁹+4¹⁰⁰  chứng tỏ A chia hết cho 5

Giúp mình nhanh nha

Answer 1

\(A=4+4^2+4^3+...+4^{99}+4^{100}\)

\(A=4\cdot\left(1+4\right)+4^3\cdot\left(1+4\right)+...+4^{99}\cdot\left(1+4\right)\)

\(A=4\cdot5+4^3\cdot5+...+4^{99}\cdot5\)

\(A=5\cdot\left(4+4^3+...+4^{99}\right)⋮5\left(đpcm\right)\)