# Sequencing Genome, I mean Limits

Calculus Level 3

Let $$a = \min (x^2+2x+3)$$ and $$b = \displaystyle \lim_{x \to 0} \frac { \sin x \ \cos x}{e^x - e^{-x} }$$ for real parameter $$x$$.

What is the value of $$\displaystyle \sum_{r=0}^n a^r b^{n-r}$$?