Sequencing Genome, I mean Limits

Calculus Level 3

Let a=min(x2+2x+3)a = \min (x^2+2x+3) and b=limx0sinx cosxexexb = \displaystyle \lim_{x \to 0} \frac { \sin x \ \cos x}{e^x - e^{-x} } for real parameter xx.

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


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