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Evaluate the indefinite integral as a power series. What is the radius of convergence?$ \int \frac {t}{1 + t^3} dt $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Campbell University

Baylor University

University of Michigan - Ann Arbor

Boston College

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.

02:28

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

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Evaluate the indefinite in…

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$25-28$ Evaluate the indef…

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you value the indefinite in the girl as a power Siri's. And what is the readers of convergence? All right, so if we're going to expand these any girl as a power Siri's so we can just live t here and we expand one plus Team Cube. So that's going to be t to the power three end and from zero to infinity and the tea. So this's equivalent to signal. And from zero to infinity T departments three impasse won TT And here we require that cube It is apple. Less than one increases on minus one, which means the developed is less than one inch means or equals one. You release components. Lessees are all right. And here everything's changed, the other integral in summation drink us won tt So, uh, this is gonna be We're integral this part. So it becomes teaching our three M plus two overthrew impasse itude yet and our is equals to one. All right,

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