The sum of the series $\displaystyle \sum_{r = 0}^{n} (-1)^{r}\ ^{n}C_{r} \left (\dfrac {1}{2^{r}} + \dfrac {3^{r}}{2^{2r}} + \dfrac {7^{r}}{2^{3r}} + \dfrac {15^{r}}{2^{4r}} + ... m\ terms \right )$ is
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$\dfrac {2^{mn - 1}}{2^{mn}(2^{n} - 1)}$
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$\dfrac {2^{mn} - 1}{2^{n} - 1}$
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$\dfrac {2^{mn} + 1}{2^{n} + 1}$
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None of these
A
Correct answer
Explanation
The series is a sum of geometric series inside a binomial expansion. The expression simplifies using the identity for the sum of binomial coefficients with alternating signs. The result is a known form for this type of series expansion.