Đặt `a,A=2+2^2+2^3+......+2^{100}`
`A=(2+ 2^2+2^3+2^4)+......+(2^{97}+2^{98}+2^{99}+2^{100})`
`A=2.(1+2+2^2+2^3)+.....+2^{97}.(1+2+2^2+2^3)`
`A=2.15+...........+2^{97}.15`
`A=15.(2+.....+2^{97})` $\vdots$ `5`
`b,`A=2+2^2+2^3+......+2^{100}`
`A=(2+2^2+2^3+2^4+2^5)+......+(2^{96}+2^{97}+2^{98}+2^{99}+2^{100})`
`A=2.(1+2+2^2+2^3+2^4)+.....+2^{96}.(1+2+2^2+2^3+2^4)`
`A=2.31+.....+2^{96}.31`
`A=31.(2+....+2^{96})` $\vdots$ `31`