If S denotes the sum to infinity and S_n, the sum of n terms of the series$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots ,\text{ such that }\mathrm{S}-{\mathrm{S}}_{\mathrm{n}}<\frac{1}{1000}$ then the least value of n is