CHÚC BẠN HỌC TỐT!!!!

a, `B=3.(1+3+3^2+....+3^{119})`

`=>B` $\vdots$ `3` 

b, `B= 3+3^2+3^3+...+3^120`

`B=(3+3^2)+(3^3+3^4)+....+(3^{119}+3^{120})`

`B=3.(1+3)+3^3(1+3)+....+3^{119}.(1+3)`

`B=3.4+3^3.4+......+3^{119}.4`

`B=4(3+3^3+.....+3^{119})`

`=>B` $\vdots$ `4`

c,`B = 3+3^2+3^3+...+3^120`

`B=(3+3^2+3^3)+(3^4+3^5+3^6)+.....+(3^{118}+3^{119}+3^{120})`

`B=3(1+3+9)+3^4(1+3+9)+.......+3^{118}(1+3+9)`

`B=3.13+3^4.13+......+3^{118}.13`

`B=13.(3+3^4+.....+3^{118})`

`=>B` $\vdots$ `13`

CHÚC BẠN HỌC TỐT!!!!

 

Cho `B = 3 + 3^2 + 3^3 + ... + 3^120`

Chứng minh rằng:

`b, B = 3 + 3^2 + 3^3 + ... . + 3^120`

`⇒ B = ( 3 + 3^2 ) + ( 3^3 + 3^4 ) + ... + ( 3^119 + 3^120 )`

`⇒ B = 3 ( 1 + 3 ) + 3^3 ( 1 + 3 ) + ... + 3^119 ( 1 + 3 )`

`⇒ B = 3 . 4 + 3^3 . 4 + ... + 3^119 . 4`

`⇒ B = 4 ( 3 + 3^3 + ... + 3^119 )`

`⇒ B ⋮ 4`

`=> Đpcm`