Explanation Concept Used: If lim n → ∞ a n exists and is finite we say that the sequence is convergent . If lim n → ∞ a n doesn’t exist or is infinite we say the sequence diverges . The given sequence is { a n } = { ( 1 + e n ) 2 n } Observe that: lim n → ∞ a n = lim n → ∞ ( 1 + e n ) 2 n using the exponent rule: a x = e ln (

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 8, Problem 8SP

To determine

To find: if the given sequence diverges or converges, and if it converges then find it’s limit. {(1+ e n)2n} .

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Chapter 8, Problem 7SP

Chapter 8, Problem 9SP

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Book Problem 15 Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV". an= b₁ = (-1)"n³ 2n5+8n² + 2 (-1)"n7 2n7+8n²+2

1. Write the first four terms of the sequence given by (−1)” (2n +1)² [° 22n-1 + (−1)n+¹ n=1 If it converges, find the value of its limit.

Please answer Questions 1 and 2 in the attached file. You don't have to answer the rest. Please give a detailed explanation of the answer.

Chapter 8 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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if the given sequence diverges or converges, and if it converges then find it’s limit. { ( 1 + e n ) 2 n } .

Solution Summary: The author explains that if the given sequence diverges or converges then find it's limit.

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To find: if the given sequence diverges or converges, and if it converges then find it’s limit. {(1+ e n)2n} .

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Chapter 8 Solutions