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Find the sum $\sum_{n=2}^\infty \dfrac{\pi^n}{n!}$.
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Find the Taylor series for $f(x) = 1 + x + x^2$ centered at $a = 2$.
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Write the Maclaurin series for $f(x) = \frac{1}{x}$ centered at $a = 5$.
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Find a power series (centered at 0) for $f(x) = e^{-3x^3}$.
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Estimate $\cos{(0.1)}$ using the 4th-degree Taylor polynomial $p_4(x)$ for $\cos{x}$.