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Use power series operations to find the Taylor series at $x=0$ for the functions in Exercises $11-28 .$

$$\frac{x^{2}}{2}-1+\cos x$$

$\sum_{n=2}^{\infty} \frac{(-1)^{n}}{(2 n) !} x^{2 n}$

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Missouri State University

Campbell University

University of Michigan - Ann Arbor

Idaho State University

So let's start with recalling what the tailor Siri's expended about. Zero for co sign. Is this negative one to the end, and then we have a two n factorial in the bottom X to the to end. And now I noticed that what we're trying to do here, we're trying to find the Taylor series expansion about zero again, but noticed that this is the first two terms of the tailor Siris for co sign. So all we need to do is adjust where we're starting R. Taylor Siri's. We're starting with the, um, with n equals 22 as opposed to an equal zero, and we're doing