1/2+1/4+1/8+...+1/512=?....the terms int his sequence are in Geometric progression,

first term a1 = 1/2

r = a(n+1)/a(n) = 1/2

number of terms (n) = 512/2 = 256

Sum or n terms in GP is given by a1(1-r^n)/1-r

= 1/2*[1-1/2^256]/1-1/2 = 1-1/2^256.

Hence, IMO it is B.