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.

$$ \frac {1}{1 \cdot 2} - \frac {1}{3 \cdot 2^3} + \frac {1}{5 \cdot 2^5} - \frac {1}{7 \cdot 2^7} + \cdot \cdot \cdot $$

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

Missouri State University

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.

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.

02:10

Find the sum of the series…

00:48

Find the sum of the given …

01:41

Find the sum for each seri…

02:09

01:38

Sum the infinite series $1…

01:48

01:46

03:44

Find the sum of $n$ terms …

01:04

Sum the infinite series $\…

08:46

Sum the series $1 \cdot 3^…

Okay. So fun that some of the Siri's and the missus tickle too Sigma One half to the power of two and minus one over two months one and ends from once You infinity It looks. It looks very similar to one of our familiar tear Siri's Which one's that's. We can recall that our attendant X equals two x minus X cube over three plus extra power five or five and ah so Ong and equals two extra car too. And once one over two months, one times not you want to. The power of money is all here with you have that you wanted out minus one yet So it is just park attendant one half moose.

View More Answers From This Book

Find Another Textbook

Kaitlyn solved the equation for x using the following calculations. Negative…

02:04

Jack had 4 hours of school. He spent 45 minutes in the library and 12 hour o…

01:11

Two milk cans have 60 and 165 litres of milk . Find a can of maximum capacit…

03:27

In a survey conducted on a group of 1800 people it is found that 1200 people…

Length of a rectangular Swimming pool is 5/2 times its breadth. Its perimete…

02:26

Find the quotient of 4.13 x 10^-8 and 0.04 x 10^5. In two or more complete s…

05:05

If nPr = 3024 and nCr = 126 then find n and r.

01:18

The volume of a cube in 4913m³. Find the length of its side and its perimete…

01:05

In a school assembly there are as many number of student in a row as the num…

01:55

How much amount is required to be invested every year so as to accumulate Rs…