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WZ
Numerade Educator

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Problem 24 Medium Difficulty

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 $

Answer

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

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