7. Apply the test for divergence to each infinite series given below. Then using at least one complete sentence, explain the conclusion of this test. (a) (b) ∞ n=1 on n² Σ* en n=1 సి/డ
7. Apply the test for divergence to each infinite series given below. Then using at least one complete sentence, explain the conclusion of this test. (a) (b) ∞ n=1 on n² Σ* en n=1 సి/డ
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please solve the following calc 2 question
![Transcription:
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7. Apply the test for divergence to each infinite series given below. Then using at least one complete sentence, explain the conclusion of this test.
(a) \[ \sum_{n=1}^{\infty} \frac{e^n}{n^2} \]
(b) \[ \sum_{n=1}^{\infty} \frac{\sqrt{3}}{e^n} \]
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Explanation:
This task is to determine whether each given infinite series converges or diverges by applying the test for divergence.
- In part (a), the series involves the exponential expression \(\frac{e^n}{n^2}\). The divergence test would examine whether the terms of the series approach zero as \(n\) approaches infinity.
- In part (b), the series involves the expression \(\frac{\sqrt{3}}{e^n}\). Again, by applying the divergence test, you should determine if these terms approach zero as \(n\) approaches infinity, which would be a hint towards convergence or divergence according to the test result.
For each case, an explanation should accompany the conclusion of the divergence test.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F530fe1a6-7788-4646-897a-9ecd9c866e6d%2F4b1ee4b2-a164-41b0-9d26-694e2794d46d%2Fijd62m_processed.png&w=3840&q=75)
Transcribed Image Text:Transcription:
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7. Apply the test for divergence to each infinite series given below. Then using at least one complete sentence, explain the conclusion of this test.
(a) \[ \sum_{n=1}^{\infty} \frac{e^n}{n^2} \]
(b) \[ \sum_{n=1}^{\infty} \frac{\sqrt{3}}{e^n} \]
---
Explanation:
This task is to determine whether each given infinite series converges or diverges by applying the test for divergence.
- In part (a), the series involves the exponential expression \(\frac{e^n}{n^2}\). The divergence test would examine whether the terms of the series approach zero as \(n\) approaches infinity.
- In part (b), the series involves the expression \(\frac{\sqrt{3}}{e^n}\). Again, by applying the divergence test, you should determine if these terms approach zero as \(n\) approaches infinity, which would be a hint towards convergence or divergence according to the test result.
For each case, an explanation should accompany the conclusion of the divergence test.
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