Đặt `A=1/3+2/3^2+3/3^3+...+100/3^100`
`3A=1+2/3+3/3^2+...+100/3^99`
`2A=1+2/3+3/3^2+...+100/3^99-(1/3+2/3^2+3/3^3+...+100/3^100)`
`2A=1+2/3-1/3+3/3^2-2/3^2+...+100/3^99-99/3^99-100/3^100`
`2A=1+1/3+1/3^2+1/3^3+...+1/3^99-100/3^100`
`2A=1-100/3^100+(1/3+1/3^2+1/3^3+...+1/3^99)`
Đặt `B=1/3+1/3^2+1/3^3+...+1/3^99`
`3B=1+1/3+1/3^2+..+1/3^98`
`2B=1+1/3+1/3^2+...1/3^98-(1/3+1/3^2+1/3^3+...+1/3^99)`
`2B=1-1/3^99`
`B=1/2-1/(3^99 .2)`
`⇒2A=1-100/3^100+1/2-1/(3^99 .2)`
`2A=1+1/2-100/3^100-1/(3^99 .2)`
`⇒2A<1+1/2`
`⇒A<3/4`
