`A= 1+ 4 + 4^2 +... + 4^99`
`4A =4( 1+ 4 + 4^2+...+4^99)`
`4A= 4 + 4^2+ 4^3+...+4^100`
`4A-A= 4 + 4^2+ 4^3 +...+4^100 - 1 -4 -4^2 -...-4^99`
`3A= 4^100 -1`
`A= (4^100 -1)/3`
Ta có: `B= 4^100 => B/3 = 4^100/3`
Mà `(4^100-1)/3 < (4^100)/3`
`=>A < B/3`
Vậy `A< B/3`