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Determine whether the series converges or diverges.$ \displaystyle \sum_{n = 1}^{\infty} \frac {1}{\sqrt [3]{3n^4 + 1}} $

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Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 4

The Comparison Tests

Sequences

Series

Oregon State University

Harvey Mudd College

Baylor 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.

02:18

Determine whether the seri…

03:20

01:07

03:56

05:52

less determined whether the Siri's convergence or diverges now, since three into the fourth plus one, is bigger than three into the fourth. This means at the Q brew is also larger. But this means that if I flip both sides and after flipped inequality as well, therefore over here, I could actually just use less than I guess, because I am going to infinity. I should put equals just in case they're they're both infinity, So one over Q Brew of three. Answer the fourth. Now let's go in and simplify this. So that's our P value. We see that we have a P series here and equals one to Infinity won over the humor of three times and so the for over three. So this convergence by the Peters with P equals for over three, and that's bigger than one. So by the comparison test, our Siri's also emerges, and that's your final answer.

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