$$\mathop {\lim }\limits_{x \to {0^ + }} ({x^n}\ln x),\,n > 0$$

The limit of the interior angle of a regular polygon of n sides as n $$ \to $$ $$\infty $$ is

$$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$

Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over {{\theta ^2}}}$$. Then $$\sum\limits_{r = 0}^n {{a^r}{b^{n - r}}} $$ is