Question

[︵✿ ๖ۣۜAαɾσɦĭ ๖ۣۜKαʂʂɦүαρ‿✿]

CMR

A=1+5+5^2+5^3+......+5^98+5^99 chia hết cho 6

B=1+5+5^2+5^3+......+5^99+5^100 ko chia hết cho 6

Answer 1

[Sooya]

\(A=1+5+5^2+5^3+...+5^{99}\)

\(A=\left(1+5\right)+\left(5^2+5^3\right)+...+\left(5^{98}+5^{99}\right)\)

\(A=6+5^2\cdot6+...+5^{98}\cdot6\)

\(A=6\left(1+5^2+...+5^{98}\right)⋮6\)

\(B=1+5+5^2+5^3+...+5^{100}\)

\(B=\left(1+5\right)+\left(5^2+5^3\right)+...+\left(5^{98}+5^{99}\right)+5^{100}\)

\(B=6+6\cdot5^2+...+6\cdot5^{98}+5^{100}\)

\(B=6\left(1+5^2+...+5^{98}\right)+5^{100}\)

a ⋮ c; b không chia hết cho c => a + b  không chia hết cho c