Question

Chứng minh rằng : A = 5^1+5^2+5^3+...+5^20 chia hết cho 6

Answer 1

A=5^1+5^2+5^3+...+5^20

=(5^1+5^2)+(5^3+5^4)+...+(5^19+5^20)

=(5+5^2)+(5^2.5+5^2+5^2)+...+(5.5^18+5^2+5^18)

=(5^2+5^1).(5^2+...+5^18)

=30.(5^2+...+5^18)

=>Achia hết cho 6

Answer 2

A=5+5²+5³+...+5²⁰

A=(5+5²)+(5³+5⁴)+...+(5¹⁹+5²⁰)

A=5.(1+5)+5³.(1+5)+...+5¹⁹.(1+5)

A=5.6+5³.6+...5¹⁹.6

A=6.(5+5³+...+5¹⁹)

Vì: 6⋮6 nên 6.(5+5³+...+5¹⁹)⋮6

Vậy: A⋮6