Question

Determine whether the sequence converges or diverges. If it converges, find the limit. $a_{n}=\frac{5}{n+2}$

Name: Problem 27, Chapter 11: Calculus: Early Transcendentals, Metric Edition
Uploaded: 2023-07-06T21:00:38-08:00
Duration: 2 min 8 s
Channel: William Semus
Description: Determine whether the sequence converges or diverges. If it converges, find the limit. an=(5)/(n+2)

   Determine whether the sequence converges or diverges. If it converges, find the limit. 
$a_{n}=\frac{5}{n+2}$

Calculus: Early Transcendentals, Metric Edition

James Stewart,… 9th Edition

Chapter 11, Problem 27

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Solved by Expert William Semus

07/06/2023

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Determine whether the sequence converges or diverges. If it converges, find the limit. $a_{n}=\frac{5}{n+2}$

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Key Concepts

Sequence

A sequence is an ordered list of numbers, where each number is associated with a natural number index. Understanding sequences is essential for analyzing patterns and behaviors within mathematics, especially in calculus and analysis.

Convergence of a Sequence

Convergence refers to a sequence’s tendency to approach a specific value, known as the limit, as the index increases indefinitely. Determining whether a sequence converges or diverges is a fundamental aspect of studying infinite processes.

Limit of a Sequence

The limit of a sequence is the value that the sequence’s terms get arbitrarily close to as the index grows without bound. This concept is critical in calculus for understanding long-term behavior and solving problems related to continuity and approximation.

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