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
Determine whether the series is convergent or divergent. If it is convergent, find its sum.$ \frac {1}{3} + \frac {1}{6} + \frac {1}{9} + \frac {1}{12} + \frac {1}{15} + \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 J Hardin
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 2
Series
Sequences
Harvey Mudd College
Baylor University
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.
02:19
Determine whether the seri…
01:40
05:31
02:59
04:25
02:18
let's determine whether the Siri's is conversion or diversion, and if it is, conversion will go ahead and find some as well. So this Siri's, we can go ahead. And if it did converse, we should just be able to pull out of one over three and rewrite. This is and so on. However, the Siri's and the inside of the parentheses. We can rewrite this as the sum and equals one to infinity of one over end. If you want, you could think of this. One is one over one. But as mentioned in your textbook, this is a well known example. Call the harmonic series, and this one actually diverges. And if you take a diversion, Siri's and if you multiply it by one over three, it'LL still that verge. Though this whole thing here diverges, and therefore this sum that was given to us will also die average. So that version, and that's our final answer
View More Answers From This Book
Find Another Textbook
05:20
a. What is accounting and how does it help you manage your personal finances…
01:42
Arnell Industries has just issued $50 million in debt (at par). The firm wil…
01:21
Calculate the future value of $1,000 invested at 5% for 5 years. Round to th…
02:35
in an arithmetic sequence, the 15th term is 48 and the 40th term is 223. Det…
00:05
Last month The Sweet Tooth Candy Shops had total sales, including sales tax,…
00:38
A random sample of 10 subjects have weights with a standard deviation of 11.…
A successful basketball player has a height of 6 feet 10 inches, or 208 cm. …
00:50
a. While still in the hospital, the doctor writes an order for an antibiotic…
09:17
From a group of 12 boys and 10 girls, a committee of 4 students are chosen a…
01:01
A small telecommunications company invested its 2010 net income of $456,700 …