Download the App!

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

Question

Answered step-by-step

Find the sum of the series.

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

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Yiming Zhang

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Sequences

Series

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.

02:56

Find the sum of the series…

02:43

02:02

02:50

04:35

00:56

Find sum of the series su…

01:53

Find the sum of the given …

01:45

01:02

00:49

02:31

Okay, fund this Some of the Siri's s. So this is Look, this looks very similar to our exponential function. But of course, we're gonna do some, like some change wearables to make it look similar to eat a power X. So is this him too? And from zero to Philly and minus one times except for four to the powers in Over in factorial. And let's see if we change t equals not you extra port for And this is just so it is Pete to the poor tea. So it was to eat. Report, Not you. Oh four. And this is our results. Shakespeare. Nothing. That's two for four.

View More Answers From This Book

Find Another Textbook

03:11

The diagram shows a shape ABCDE_ The shape iS made from a rectangle, a right…

01:01

What is the vertex for the graph below?0 A (5,0)B. (3,0)C. (1,4)…

05:20

The line RCT is a tangent to the circle.angle ADC = 1370 angle OCB = 350…

00:55

What is the sample size if the population is 2000 and the margin of error is…

02:21

The length of an arc of a circle is 12cm. The corresponding sector area is 1…

02:00

Use the diagram below: Tell whether the angles are vertical angles; linear p…

01:25

The table below shows the three-day rain forecast for Friday; Saturday and S…

01:27

Use the functions f(x) and g(x) to complete the comparison statements using …

03:00

The height of a triangle is 1.95 centimeters less than 2.5 times the corresp…

01:26

the equation of a line in slope-intercept form that has a positive a. Write …