Let $a =$ Minimum $\{x^2 + 2x + 3, x \in R\}$ and $b = \mathop {\lim }\limits_{\theta  \to 0} \frac{{1 - \cos \theta }}{{{\theta ^2}}}$ The value of $\sum\limits_{r = 0}^n {{a^r}.{b^{n - r}}} $ is

  • A

    $\frac{{{2^{n + 1}} - 1}}{{{{3.2}^n}}}$

  • B

    $\frac{{{2^{n + 1}} + 1}}{{{{3.2}^n}}}$

  • C

    $\frac{{{4^{n + 1}} - 1}}{{{{3.2}^n}}}$

  • D

    None of these

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