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Determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 3}^{\infty} n^{-0.9999} $

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The series is divergent.

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Sequences

Series

Missouri State University

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.

05:26

Determine whether the seri…

02:06

02:32

01:12

01:06

01:55

and this problem. We have Thio to determine if a specific Siri's is convergent or divergent. So we're given the Siri's from n equals three to Infinity off and raised to negative 30.9999 Well, we should recognize the format of this Siri's. This is a P Siri's, and in this case, RPI value is 0.9999 Well, that is less than or equal toe one. So what we can say using the P Siri's test is that this series is divergent. So I hope that this problem helped you understand not only how we can recognize a P Siri's, but also how we can use the P Siri's test to understand if a Siri's is divergent.

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