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Sum of the series $\sum_{r = 0}^{10} (- 1)^{r} (^{10} C_{r}) [\frac{1}{2^{r}} + \frac{3^{r}}{2^{2 r}}]$ is

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210+1220

210-1220

220-1220

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Correct option is A

∑r=010 (−1)r 10Cr12r+3r22r=1−1210+1−3410=210+1220

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Sum of the series ∑r=010 (−1)r 10Cr12r+3r22r is

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Sum of the series $\sum_{r = 0}^{10} (- 1)^{r} (^{10} C_{r}) [\frac{1}{2^{r}} + \frac{3^{r}}{2^{2 r}}]$ is