Ta có :
`A(x) = x + x^2 +x^3 + ... + x^100`
`-> A(1/2) = 1/2 + 1/2^2 +1/2^3 + ... +1/2^100`
`-> 1/2A(1/2) = 1/2^2 + 1/2^3 + 1/2^4 + ... +1/2^101`
`-> A(1/2) - 1/2A(1/2) = ( 1/2 + 1/2^2 +1/2^3 + ... +1/2^100) - ( 1/2^2 + 1/2^3 + 1/2^4 + ... +1/2^101)`
`-> 1/2A(1/2) =1/2- 1/2^101`
`-> A(1/2) = (1/2-1/2^101) : 1/2 = 2(1/2-1/2^101)`
`-> A(1/2) = 1-1/2^100`