ko tính tổng,hãy giải thích: 3^3+3^4+3^5+3^6 chia hết cho 4 5^5+5^6+5^7+5^8 chia hết cho 6

`3^3 + 3^4+3^5+3^6`

`= (3^3 + 3^4) + (3^5+3^6)`

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

`=  3^3 . 4 + 3^5 .4`

`= 4 . (3^3 + 3^5)`

`=> 3^3 + 3^4+3^5+3^6` $\vdots$ `hết` `cho` `4`

`5^5 + 5^6 +5^7+5^8`

`= (5^5 + 5^6) + (5^7+5^8)`

`= 5^5 .( 1+5) + 5^7 . ( 1+5)`

`=  5^5 . 6 + 5^7 . 6`

`= 6 . (5^5 + 5^7)`

`=>5^5 + 5^6 +5^7+5^8` $\vdots$ `hết` `cho` `6`

Đáp án:

`3^3`+`3^4`+`3^5`+`3^6 `

=(`3^3`+`3^4`)+(`3^5`+`3^6`) 

=`3^3`(`1+3`)+`3^5`(`1+3`) 

=(`3^3`+`3^5`)(`1+3`) 

=(`3^3`+`3^5`)`.4`

Mà `4` $\vdots$ `4 `

⇒`3^3`+`3^4`+`3^5`+`3^6` $\vdots$ `4`

`5^5`+`5^6`+`5^7`+`5^8 `

=(`5^5`+`5^6`)+(`5^7`+`5^8`)

=`5^5`(`1+5`)+`5^7`(`1+5`)

=(`5^5`+`5^7`)(`1+5`)

=(`5^5`+`5^7`)`.6`

Mà `6` $\vdots$ `6`

⇒`5^5`+`5^6`+`5^7`+`5^8` $\vdots$ `6`