Explanation Given: ∑ n = 1 ∞ n 3 a n | a n + 1 a n | converges to ρ = 1 3 Formula Used: We will find out, the given series converges or diverges using Ratio Test for Series: Let, L = lim n → ∞ | a n + 1 a n | If L<1, then the series ∑ n = 1 ∞ a n converges. If L>1, then the series ∑ n = 1 ∞ a n diverges. If L=1, then the series is inconclusive. Calculation: We have been given ∑ n = 1 ∞ n 3 a n . To show that the given series converges or diverges, let’s use Ratio Test for Series...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 11.5, Problem 29E

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To check: whether $\sum_{n = 1}^{\infty} n^{3} a_{n}$ converges, assuming $| \frac{a_{n + 1}}{a_{n}} |$ converges to $ρ = \frac{1}{3}$ .

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Chapter 11.5, Problem 28E

Chapter 11.5, Problem 30E

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Chapter 11 Solutions

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Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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To check: whether ∑ n = 1 ∞ n 3 a n converges, assuming | a n + 1 a n | converges to ρ = 1 3 .

Solution Summary: The author analyzes how the given series converges using Ratio Test for Series.

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To check: whether $\sum_{n = 1}^{\infty} n^{3} a_{n}$ converges, assuming $| \frac{a_{n + 1}}{a_{n}} |$ converges to $ρ = \frac{1}{3}$ .

Want to see the full answer?

Chapter 11 Solutions

To check: whether ∑ n = 1 ∞ n 3 a n converges, assuming | a n + 1 a n | converges to ρ = 1 3 .

Solution Summary: The author analyzes how the given series converges using Ratio Test for Series.

Videos

To check: whether ∑n=1∞n3an converges, assuming |an+1an| converges to ρ=13.

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Chapter 11 Solutions

To check: whether $\sum_{n = 1}^{\infty} n^{3} a_{n}$ converges, assuming $| \frac{a_{n + 1}}{a_{n}} |$ converges to $ρ = \frac{1}{3}$ .