Tham khảo
Đặt `S=2+2^2+2^3+2^4+....+2^{100}`
`⇒S+5=(2+5)+(2^2+2^3+2^4)+...+(2^{98}+2^{99}+2^{100})`
`⇒S+5=7+2.(2+2^2+2^3)+....+2^{97}.(2+2^2+2^3)`
`⇒S+5=7+(2+2^2+2^3).(2+...+2^{97})`
`⇒S+5=7+14.(2+..+2^{97})`
Vì `7 \vdots 7,14 \vdots 7⇒14.(2+..+2^{97}) \vdots 7`
Do đó `7+14.(2+..+2^{97}) \vdots 7`
hay `S+5 \vdots 7`
`\text{©CBT}`