a) `A= 1/2 - 1/4 + 1/8 -1/16+ 1/32 - 1/64`
`A= 1/2 - 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6`
`1/2 A = 1/2(1/2 - 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6)`
`1/2 A= 1/2^2 - 1/2^3 + 1/2^4 - 1/2^5 + 1/2^6 - 1/2^7`
`1/2 A + A = 1/2^2 - 1/2^3 + 1/2^4 - 1/2^5 + 1/2^6 - 1/2^7 + 1/2 - 1/2^2 + 1/2^3 - 1/2^4 + 1/2^5 - 1/2^6`
`3/2 A = 1/2 - 1/2^7`
`A = (1/2 - 1/2^7) : 3/2`
`A= (1/2 - 1/2^7) . 2/3`
`A= 1/3 - 1/(2^6 .3) < 1/3`
Vậy `A< 1/3`
b) `B= 1 -1/3 + 1/3^2 - 1/3^3 +...- 1/3^99`
`1/3 B = 1/3( 1 -1/3 + 1/3^2 - 1/3^3 +...- 1/3^99)`
`1/3 B = 1/3 - 1/3^2 + 1/3^3- 1/3^4 +...- 1/3^100`
`1/3 B+ B= 1/3 - 1/3^2 + 1/3^3- 1/3^4 +...- 1/3^100 + 1 -1/3 + 1/3^2 - 1/3^3 +...- 1/3^99`
`4/3 B = 1 - 1/3^100`
`B= ( 1- 1/3^100) : 4/3`
`B= ( 1 - 1/3^100) . 3/4`
`B= 3/4 - 1/(3^99 . 4) < 3/4`
Vậy `B< 3/4`
