Solve this:

​Q1. Let a = min  [x² + 2x + 3 , x $\in \mathrm{R}$] and b = $\underset{\mathrm{\theta }\to 0}{\mathrm{Lim}}\frac{1-\cos \mathrm{\theta }}{{\mathrm{\theta }}^2}$. The value of $\sum _{\mathrm{r} =0}^{\mathrm{n}} {\mathrm{a}}^{\mathrm{r}} .{\mathrm{b}}^{\mathrm{n}-\mathrm{r}}$ is 

      $\left(\mathrm{A}\right) \frac{2^{\mathrm{n}+1}-1}{3.2^{\mathrm{n}}} \left(\mathrm{B}\right) \frac{2^{\mathrm{n}+1} +1}{3.2^{\mathrm{n}}} \left(\mathrm{C}\right) \frac{4^{\mathrm{n}+1} -1}{3.2^{\mathrm{n}}}$ (D) none of these