$\\$
`B=1/2+(1/2)^2+...+(1/2)^{99}`
`->1/2 B =(1/2)^2+(1/2)^3+...+(1/2)^{100}`
`->B-1/2B = [1/2+(1/2)^2+...+(1/2)^{99}]-[(1/2)^2+(1/2)^3+...+(1/2)^{100}]`
`-> 1/2 B = 1/2 - (1/2)^{100}`
`->B = (1/2 - 1/2^{100}) . 2`
`->B = 1 - 1/2^{99}`
Vậy `B=1-1/2^{99}`