The sum of the first n terms of the series \(\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{{15}}{{16}} + \ldots \) is equal to
1
\({{\rm{2}}^{\rm{n}}}{\rm{-\;n - 1}}\)
2
\({\rm{1-}}\;{{\rm{2}}^{{\rm{ - n}}}}\)
3
\({{\rm{2}}^{{\rm{ - n}}}}{\rm{ + \;n - 1}}\)
4
\({{\rm{2}}^{\rm{n}}}{\rm{ - 1}}\)