If \( \sum_{r=0}^{n}(-1)^{r}{ }^{n} C_{r}\left[\frac{1}{2^{r}}+\frac{3^{r}}{2^{2 r}}+\frac{7^{r}...

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If \( \sum_{r=0}^{n}(-1)^{r}{ }^{n} C_{r}\left[\frac{1}{2^{r}}+\frac{3^{r}}{2^{2 r}}+\frac{7^{r}}{2^{3 r}}+\ldots\right. \) upto \( m \) terms \( ] \) \( =f(n)\left(1-\frac{1}{2^{m n}}\right) \)
\( \int_{-3}^{3} f\left(x^{3} \ln x\right) d\left(x^{3} \ln x\right) \) is equal to
(a) \( -6 \)
(b) \( -3 \)
(c) 3
(d) Cannot be determined
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