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Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

$ f(x) = \sin (\pi x/4) $

$\sum_{n=0}^{\infty}(-1)^{n} \frac{\left(\frac{\pi x}{4}\right)^{2 n+1}}{(2 n+1) !}, \quad R=\infty$

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University of Illinois at Urbana-Champaign