a,
`M=3+3^2+3^3+.....+3^100`
`=(3+3^2)+(3^3+3^4)+.....+(3^99+3^100)`
`=3(1+3)+3^3(1+3)+.....+3^99(1+3)`
`=3·4+3^3·4+.....+3^99·4`
`=4(3+3^3+.....+3^99)\vdots4`
`=>M\vdots4`
Mặt khác
`M=3+3^2+3^3+3^4+.....+3^100`
`=(3+3^3)+(3^2+3^4)+...+(3^98+3^100)`
`=3(3+3^2)+3^2(3+3^2)+.....+3^98(3+3^2)`
`=3·12+3^2·12+.....+3^98·12`
`=12(3+3^2+.....+3^98)\vdots12`
`=>M\vdots12`
b,
`M=3+3^2+3^3+.....+3^100`
`=>3M=3^2+3^3+3^4+.....+3^101`
`=>3M-M=(3^2+3^3+.....+3^101)-(3+3^2+3^3+.....+3^100)`
`=>2M=3^101-3`
`=>M=(3^101-3)/2`
Ta có:
`2·M+3=3^n`
`<=>2·(3^101-3)/2+3=3^n`
`<=>3^101-3+3=3^n`
`<=>3^101=3^n`
`<=>n=101`
$#Chúc bạn học tốt$
