Question

Chứng minh rằng : \(\left(2005+2005^2+2005^3+...+2005^{10}\right)\) chia hết cho 2006

Answer 1

2005+2005²+2005³+...+2005¹⁰

=2005.(1+2005)+2005³.(1+2005)+...+2005⁹.(1+2005)

=2005.2006+2005³.2006+...+2005⁹.2006

=2006.(2005+2005³+...+2005⁹)

=>2005+2005²+2005³+...+2005¹⁰ chia hết cho 2006

Answer 2

= 2005.(1+2005)+2005².(1+2005)+...+2005⁹.(1+2005)

= 2006.(2005+2005²+...+2005⁹) 

=> tổng trên chia hết cho 2006

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