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# Find the Taylor series for $f(x)$ centered at the given value of $a.$ [Assume that $f$ has a power series expansion. Do not show that $R_n (x) \to 0.$] Also find the associated radius of convergence.$f(x) = \cos x,$ $a = \pi/2$

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

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