Question

CM: 2004+2004²+2004³+...+2004¹⁰ chia hết cho 2005

Answer 1

tham khảo ở link: https://olm.vn/hoi-dap/detail/87851120650.html

 

Answer 2

Đặt A=2004+2004²+2004³+...+2004¹⁰

         =(2004+2004²)+(2004³+2004⁴)+...+(2004⁹+2004¹⁰)

         =2004(1+2004)+2004³(1+2004)+...+2004⁹(1+2004)

         =2004.2005+2004³.2005+...+2004⁹.2005 chia hết cho 2005

Vậy A chia hết cho 2005.

Answer 3

Đặt A=2004+2004²+2004³+...+3004¹⁰

    A=(2004+2004²)+(2004³+2004⁴)+.....+(2004⁹+2004¹⁰⁾

      A=(2004+2004²)+2004².(2004+2004²)+...+2004⁸.(2004+2004²)

    A=4018020+2004².4018020+.....+2004⁸.4018020

     A=4018020.(1+2004²+....+2004⁸)

     A=2004.2005.(1+2004²+...+2004⁸)\(⋮\)2005

Vậy A\(⋮\)2005

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