Bài `8 `

`a)`

`5^5 - 5^4 + 5^3 `

`= 5^3 . (5^2 - 5^1 + 1)`

`= 5^3 . (25 - 5 + 1)`

`= 5^3 . 21`

Mà `21` $\vdots$ `7`

`=> 5^3 . 21` $\vdots$ `7`

`=> 5^5 - 5^4 + 5^3` $\vdots$ `7 (đpcm)`

`b)`

`A = 2 + 2^2 + 2^3 +...+ 2^(2004)`

`A = (2 + 2^2) + (2^3 + 2^4) +...+ (2^(2003) + 2^(2004))`

`A = 2.(1 + 2) + 2^3.(1 + 2) +...+ 2^(2003).(1 + 2)`

`A = 2.3 + 2^3.3 +...+ 2^(2003).3`

`A = (2 + 2^3 +...+ 2^(2003)).3`

`=> A` $\vdots$` 3 (đpcm)`

`a,5^5-5^4+5^3`

`=5^3 . (5^2-5+1)`

`=5^3 . (25-5+1)`

`=5^3 . (20+1)`

`=5^3 .21`

Do `21\vdots7->5^3 . 21\vdots7`

Hay : `5^5-5^4+5^3\vdots7(đpcm)`

`···········`

`b,A=2+2^2+2^3+...+2^2004`

`A=(2+2^2)+(2^3+2^4)+...+(2^2003+2^2004)`

`A=2.(1+2)+2^3 .(1+2)+...+2^2003 . (1+2)`

`A=2.3+2^3 . 3+...+2^2003 . 3`

`A=3.(2+2^3+...+2^2003)`

Do `3\vdots3->A\vdots3(đpcm)`

`#Sal_tSea`