Question

Cho A=5+5^2+5^3+....+5^2007

Chứng minh rằng A chia hết cho 31

 

Answer 1

Ta có A=5+5^2+5^3+...+5^2007

=(5+5^2+5^3)+(5^4+5^5+5^6)+...+(5^2005+5^2006+5^2007)

=31x5+31x5^4+...+31x5^2005

=31x(5+5^4+...+5^2005) chia hết cho 31

Vậy A chia hết cho 31

Answer 2

A = 5 + 5² + 5³ + .....+ 5²⁰⁰⁷

    = ( 5 + 5² + 5³ ) + ( 5⁴ + 5⁵ + 5⁶ ) +.........+ (5²⁰⁰⁵ + 5²⁰⁰⁶ + 5²⁰⁰⁷ )

    = 5( 1 + 5 + 5² ) + 5⁴( 1 + 5 + 5² ) +.........+ 5²⁰⁰⁵( 1 + 5 + 5² )

    = 31( 5 + 5⁴ + .....+ 5²⁰⁰⁵ )\(⋮\)31

Vậy A \(⋮\)31