Question

Cho A = 2009 + $2009^{2}$ + $2009^{3}$  + ... + $2009^{10}$ 
Chứng tỏ A ⋮ 2010  

Answer 1

bạn tham khảo

A=(2009+2009^2)+(2009^3+2009^4)+...+(2009^9+2009^10)

A=[2009.(1+2009)]+[2009^3.(1+2009)]+....+[2009^9.(1+2009)]

A=2009.2010+2009^3.2010+...+2009^9.2010

A=2010(2009+2009^3+2009^5+......+2009^9)  chia het cho 2010

Answer 2

Ta có `:`

`A=2009 + 2009^2 +....+2009^{10}`

  `= ( 2009+2009^2) +.....+(2009^9+2009^{10})`

  `= 2009*2010+.....+2009^9*2010`

  `= ( 2009+...+2009^9)*2010` \(\vdots\) `2010`

`=> A` \(\vdots\) `2010` (đpcm)