Let and . Find the value of…

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

a=\min\{x^2+2x+3:x\in\mathbb{R}\}

and

b=\lim_{\theta\to0}\frac{1-\cos\theta}{\theta^2}

. Find the value of

\sum_{r=0}^{n}a^rb^{n-r}

.

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