Ta có `:`
`S = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{99} + 1/3^{100}`
`=> 3S = 1 + 1/3 + 1/3^2 + ... + 1/3^{98} + 1/3^{99}`
`=> 3S - S = ( 1 + 1/3 + 1/3^2 + ... + 1/3^{98} + 1/3^{99} ) -`
`( 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{99} + 1/3^{100} )`
`=> 2S = 1 - 1/3^{100}`
`=> S = 1/2 - 1/( 3^{100} . 2 )`
Vậy `:` ` S = 1/2 - 1/( 3^{100} . 2 )`