Explanation Definition used: Nth Partial Sum of an Infinite Series: Let ∑ n = 1 ∞ a n = a 1 + a 2 + a 3 + ⋯ + a n + ⋯ be an infinite series and S N = ∑ n = 1 N a n = a 1 + a 2 + a 3 + ⋯ + a N be the N th partial sum of the series. If the sequence of partial sums { S N } converges to the number S . That is, if lim N → ∞ S N = S , then the series ∑ a n converges and has sum S, written as ∑ n = 1 ∞ a n = a 1 + a 2 + a 3 + ⋯ + a n + ⋯ = S . If { S N } diverges, then the series ∑ a n diverges. Calculation: The given series is ∑ n = 1 ∞ ( 1 n 2 + 3 n + 2 ) . Simplify the series ∑ n = 1 ∞ ( 1 n 2 + 3 n + 2 ) . ∑ n = 1 ∞ ( 1 n 2 + 3 n + 2 ) = ∑ n = 1 ∞ ( 1 ( n + 1 ) ( n + 2 ) ) = ∑ n = 1 ∞ ( 1 n + 1 − 1 n + 2 ) The N th partial sum of the given series ∑ n = 1 ∞ ( 1 n + 1 − 1 n + 2 ) is calculated as follows

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 11.3, Problem 3E

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To find: The Nth partial sum of the infinite series ∑n=1∞(1n2+3n+2) and evaluate its limit to determine whether the series converges or diverges; find its sum if the series is convergent.

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Chapter 11.3, Problem 2E

Chapter 11.3, Problem 4E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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The N th partial sum of the infinite series ∑ n = 1 ∞ ( 1 n 2 + 3 n + 2 ) and evaluate its limit to determine whether the series converges or diverges; find its sum if the series is convergent.

Solution Summary: The author evaluates the N th partial sum of the infinite series displaystyle 'underset' to determine whether the series converges or diverges.

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To find: The Nth partial sum of the infinite series ∑n=1∞(1n2+3n+2) and evaluate its limit to determine whether the series converges or diverges; find its sum if the series is convergent.

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Chapter 11 Solutions