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Find the first three nonzero terms of the Maclaurin series for each function and the values of $x$ for which the series converges absolutely.$$f(x)=\cos x-(2 /(1-x))$$

$$\cos x-\frac{2}{1-x} \text { is }-1-2 x-\frac{5}{2} x^{2}+\cdots$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

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.

03:35

Find the first three nonze…

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02:04

05:45

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02:05

they probably 35 for this problem. That's just confused. Victorian serious. Off course I access to over one minus x. So, yes, I am Sigma from zero to infinity. Factorial Dr. And here's, uh, uh huh to the toy on my nightstand, minus one for the end. Right, Here's our function. And to our one minus axe, it's just two times I'm class at the square, plus another so we won't want to find a first rate turn 1st 390 turns Right. So that is, uh, the first time This one. There's no second turf and certain Terminus Highness, Accident X where and here's minus two by those two acts and minus two Expert, So that's minus one. Buying this two acts and minus five over to act square. Here are just 1st 3 terms. It's where at the first returns, right? And what a fine Beachbody. All facts for the serious calm versus. So this dysfunction cover GIs when acts absolute body always Florida. What here? Cause I asked, covered his butt. Well, you are so just greater than minus one of the what? That's okay,

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