Consider the series Answer: L = ∞ 00 n=1 9n³+1 #)". Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it do 2n³+3 |an| = L lim 71-00 What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: Divergent
Consider the series Answer: L = ∞ 00 n=1 9n³+1 #)". Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it do 2n³+3 |an| = L lim 71-00 What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive". Answer: Divergent
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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![### Evaluating Series Using the Root Test
**Consider the series \(\sum_{n=1}^{\infty} \left( \frac{9n^3 + 1}{2n^3 + 3} \right)^n\). Evaluate the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".**
\[
\lim_{n \to \infty} \sqrt[n]{|a_n|} = L
\]
**Answer:** \(L = \infty\)
**What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive".**
**Answer:** Divergent
**Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".**
**Answer:** Divergent](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2F1ffe68f3-7240-4536-ace1-203b4c6d8372%2Fkf9q9ra_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Series Using the Root Test
**Consider the series \(\sum_{n=1}^{\infty} \left( \frac{9n^3 + 1}{2n^3 + 3} \right)^n\). Evaluate the following limit. If it is infinite, type "infinity" or "inf". If it does not exist, type "DNE".**
\[
\lim_{n \to \infty} \sqrt[n]{|a_n|} = L
\]
**Answer:** \(L = \infty\)
**What can you say about the series using the Root Test? Answer "Convergent", "Divergent", or "Inconclusive".**
**Answer:** Divergent
**Determine whether the series is absolutely convergent, conditionally convergent, or divergent. Answer "Absolutely Convergent", "Conditionally Convergent", or "Divergent".**
**Answer:** Divergent
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