Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Find a power series representation for $ f, $ and graph $ f $ and several partial sums $ s_n(x) $ on the same screen. What happens as $ n $ increases?$ f(x) = \ln \left( \frac {1 + x}{1 - x} \right) $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\sum_{n=0}^{\infty} \frac{2 x^{2 n+1}}{2 n+1}$

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Sequences

Series

Oregon State University

Harvey Mudd College

Baylor University

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.

02:55

Find a power series repres…

02:34

10:21

0:00

the problem is, find a power. Siri's reps of condition Oh, on the graph, half on the several partial sums as in Max on the same screen. What happens as any increases So first to behalf. Want over one last Max? Yes, he caught you some from zero to infinity. Negative acts to the part ofthe end. Then we have out in one plus X is the country's integral one over one plus x Jax. This is equal to some off from zero to twenty. Nate, you want the power and hands next to the pop off us one over and plus one plus constant number. See here accidents. Last someone absolutely a fax. It's unless someone we put ax got zero in this equation and up a time out. One plus zero is equal to C. C. Is a portal zero On behalf of Alan one last sax. It's equal to the sum of from zero to infinity. Like you want the power ofthe end times X to the power ofthe plus one over and plastic. Then how how in one minus acts is the call to some ofthe from zero to infinity makes you want the power off and you will replace Axe. I make your backs. Which is is that what you're? Some from zero to infinity next to one ham's acts to the powerful plus one over and plus what then? Off Max, If he called you out in one plus x minus. Alan one minus X This is a call to some from zero to infinity. Makes you want the power on and last one. Ham's facts to the public on plus one over plus one. This is iniquitous truth times The sum from zero to infinity Act two The part ofthe two and plus one over to hand us one. You're absolutely off. ACS is the last one. Now let's look at the graph off half a box and we can graft I Cyril a swan I us three. The partial sums a serial as one on US three not to start as any increases. As a max, the partial sums becomes a biting approximation to athletics. Oh, after a while, you off X is less somewhat

View More Answers From This Book

Find Another Textbook

Missouri State University

Campbell University

University of Nottingham