$\color{lightblue}{\text{o Lâm Vũ}}$

Bài `17`: 

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

 Ta có: $5^5$ - $5^4$ + $5^3$

$5^3$ ( $5^2$ - `5` + `1` )

$5^3$ . `21`

Mà `21` $\vdots$ `7` 

Nên $5^3$ . `21` $\vdots$ `7`

Vậy `A` $\vdots$ `7`

Bài `18`:

`a`) `C` = `1` + `2` + $2^2$ + $2^3$ + ... + $2^1$$^0$$^0$

`2C` = `2` + $2^2$ + $2^3$ + ... + $2^1$$^0$$^1$

`2C` - `C` = ( `2` + $2^2$ + $2^3$ + ... + $2^1$$^0$$^1$ ) - ( `1` + `2` + $2^2$ + $2^3$ + ... + $2^2$$^0$$^0$ )

`C` = $2^1$$^0$$^1$ - `1`

Vậy `C` = $2^1$$^0$$^1$ - `1`

`b`) `D` = `-1` + `3` + $3^2$ + ... + $3^2$$^n$ + $3^2$$^n$$^+$$^1$

`3D` = `-3` + $3^2$ + $3^3$ + ... + $3^2$$^n$$^+$$^1$ + $3^2$$^n$

`3D` - `D`  = ( `-3` + $3^2$ + $3^3$ + ... + $3^2$$^n$$^+$$^1$ + $3^2$$^n$ ) - ( `-1` + `3` + $3^2$ + ... + $3^2$$^n$ + $3^2$$^n$$^+$$^1$

`2D` = $3^2$ + `1` - `6` = $3^2$$^n$ - `5`

`D` = $3^2$$^n$ - `5` : `2`

Vậy `D` = $3^2$$^n$ - `5` : `2`