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Use the binomial series to expand the function as a power series. State the radius of convergence.

$ \sqrt [3]{8 + x} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

Campbell University

Oregon State University

University of Nottingham

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.

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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Use the binomial series to…

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the problem is hears about Nami ofthe serious trees expands of function upon Siri's stages. A regis of commitments but for my other half, first to be rewriting his function. Two hands, one last fax over it. The public want food and all manner. How this's equal to two times some time from zero tweets. Amenity. It's there. Yeah, axe to ax over. Pete the power. This is a conscious some from zero to infinity to his house. Then comes one over it to the part of end times. Thanks to parliament, cover computes the limit on cost Unity. How so? Shoot house one through eight. Here we go. One on one wine, two houses, one third and over it to the party, which is what is the limit and cost to infinity Housel Audio off one third, minus over it Hams Trust want. So this is a two one over eight. So the readers of convergence is the one true eight

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