\( \sum_{r=0}^{10}(-1)^{r}{ }^{10} C_{r}\left[\frac{1}{2^{r}}+\frac{3^{r}}{2^{2 r}}+\frac{7^{r}}...
\( \sum_{r=0}^{10}(-1)^{r}{ }^{10} C_{r}\left[\frac{1}{2^{r}}+\frac{3^{r}}{2^{2 r}}+\frac{7^{r}}{2^{3 r}}+\frac{15^{r}}{2^{4 r}}+\ldots\right]= \)
(A) \( \frac{1}{511} \)
(B) \( \frac{1}{2047} \)
(C) \( \frac{1}{1023} \)
(D) \( \frac{1}{4095} \)
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