\(\sum\limits_{r=0}^n(-1)^r \,^nC_r \left( \frac 1{2^r} + \frac{3^r}{2^{2r}} + \frac {7^r}{2^{3r}}+\frac{15^r}{2^{4r}} + ....\text{up to m terms}\right) =\)
(a) \(\frac{2^{mn}-1}{2^{mn} (2^n - 1)}\)
(b) \(\frac{2^m-2^n}{m-n}\)
(c) 1
(d) None of these