Chứng minh rằng M= 5+5^2+5^3+5^4+....5^9+5^10 chí hết cho 6

Question

tuminh2 · Answer

`M=5+5^2+5^3+...+5^9+5^10`   `=5(1+5)+5^3.(1+5)+..+5^9.(1+5)`   `=5.6+5^3 . 6+...+6.5^9`   `=6.(5+5^3+...+5^9) vdots 6`

tuyetanhthu · Answer

M = 5 + `5^2` + `5^3` + `5^4` + . . . + `5^9` + `5^10`

M = ( 5 + `5^2` ) + ( `5^3` + `5^4` ) + . . . + ( `5^9` + `5^10` )

M = 5 ( 1 + 5 ) + `5^3` ( 1 + 5 ) + . . . + `5^9` ( 1 + 5 )

M = 5 . 6 + `5^3` . 6 + . . . + `5^9` . 6

M = 6 ( 5 + `5^3` + . . . + `5^9` )

Mà 6 chia hết cho 6 `=>` M chia hết cho 6 ( đpcm ).

Chứng minh rằng M= 5+5^2+5^3+5^4+….5^9+5^10 chí hết cho 6