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Find the Taylor series generated by $f$ at $x=a$.$$f(x)=\cos (2 x+(\pi / 2)), \quad a=\pi / 4$$

$$\sum_{n=0}^{\infty}(-1)^{n+1} 2^{2 n} \frac{(x-\pi / 4)^{2 n}}{(2 n !)}$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

02:28

Find the Taylor series gen…

01:44

00:45

problem. 33 series. And they're away too. Solve this problem. That's to change the varietal. Okay, a fax is he goes to cause I max plus power too. And change of arrivals you is equals two. Thanks. Minus pi were for so when the U. S. Because who acts as pie or for but access equals to a so such that us equals to zero. Um, we know that hitter expansion we know the McCaughrean serious about when used just zero. That's why we need to change the rivals. And that's how cause I to you plus pie. And that's just the minus cause I to you and you know that Buy chlorine serious When you're zero, it's just minus ah, till you tooty too And us one find this one to the end Oh, does that twin? There's no toe Best toe Victorio and and from zero to infinity And just change you as a axe to the, uh just just changed you as x minus pi over four. So that's, uh, minus sigma When this one to the end Times 2 22 n times X minus. I work for to the tour. You ready by toe in Victoria. So here's around, sir. Take this into why this one And that's why so here is elder

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