Explanation Given: Consider the given sequence as a n = n 2 e − n . Definition used: If a n is a sequence and lim n → ∞ a n exists, then the sequence a n is said to be converges; otherwise it diverges. Laws of limits for sequences used: If f ( x ) and g ( x ) are two functions, then lim x → a [ f ( x ) g ( x ) ] = lim x → a f ( x ) lim x → a g ( x ) and lim x → a g ( x ) ≠ 0 . Calculation: Obtain the limit of the sequence to investigate whether the sequence converges or diverges. lim n → ∞ a n = lim n → ∞ ( n 2 e − n ) = lim n → ∞ ( n 2 e n ) Since ∞ ∞ is in indeterminate form, apply the L’Hospital’s Rule

Essential Calculus: Early Transcendentals

2nd Edition

ISBN: 9781133112280

Author: James Stewart

Publisher: Cengage Learning

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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 8.1, Problem 23E

To determine

Whether the sequence converges or diverges and obtain the limit if the sequence converges.

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Chapter 8.1, Problem 22E

Chapter 8.1, Problem 24E

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Chapter 8 Solutions

Essential Calculus: Early Transcendentals

Ch. 8.1 - (a) What is a sequence? (b) What does it mean to...Ch. 8.1 - Prob. 2E Ch. 8.1 - List the first six terms of the sequence defined...Ch. 8.1 - List the first nine terms of the sequence...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Find a formula for the general term an of the...Ch. 8.1 - Determine whether sequence converges or diverges....Ch. 8.1 - Determine whether the sequence converges or...

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