`C=1/3+1/3^2+1/3^3+....+1/3^100`
`⇒3C=3.(1/3+1/3^2+1/3^3+....+1/3^100)`
`⇒3C=1+1/3+1/3^2+1/3^3+....+1/3^99`
`⇒3C-C=(1+1/3+1/3^2+1/3^3+....+1/3^99)-(1/3+1/3^2+1/3^3+....+1/3^100)`
`⇒2C=1- 1/3^100`
`⇒C=(1- 1/3^100)/2`
$\color{red}{\text{@Tiểu Bạch}}$
$\color{green}{\text{@Bạch Phượng Cửu}}$