Question

A: 5+52+..+5100

a, chứng tỏ sao cho A chia hết cho 6

 

Answer 1

`A=5+5^2+...+5^100`

`=> A=(5+5^2)+(5^3+5^4)+...+(5^99+5^100)`

`=> A=6.5+6.5^3+...+6.5^99`

`=> A=6(5+5^3+...+5^99)⋮6` (đpcm)

Answer 2

A=(5+5²)+(5³+5⁴)+...+(5⁹⁹+5¹⁰⁰)

=5.(1+5)+5³.(1+5)+...+5⁹⁹.(1+5)

=5.6+5³.6+....+5⁹⁹.6

=6.(5+5³+...+5⁹⁹)

=>A chia hết cho 6

Answer 3

\(5+5^2+...+5^{100}\\ =\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{99}+5^{100}\right)\\ =5.\left(1+5\right)+5^3.\left(1+5\right)+...+5^{99}.\left(1+5\right)\\ =5.6+5^3.6+...+5^{99}.6\)

Vậy \(A⋮6\)

Answer 4

A=(5+5²)+(5³+5⁴)+...+(5⁹⁹+5¹⁰⁰)

A=5.(1+5)+5³.(1+5)+...+5⁹⁹.(1+5)

A=5.6+5³.6+....+5⁹⁹.6

A=6.(5+5³+...+5⁹⁹)

vậy A chia hết cho 6