Explanation Given: Given sequence 1 l 0 , 3 100 , 7 l 000 , l 5 10 , 000 , 31 100 , 000 , 63 1 , 000 , 000 ........ Concept Used: A sequence { a n } is said to be convergent if the n t h term of the sequence approaches unique finite as n approaches ∞ otherwise sequence said to be divergent. Calculation: As we have 1 l 0 , 3 100 , 7 l 000 , l 5 10 , 000 , 31 100 , 000 , 63 1 , 000 , 000 ........ , whose n t h term is { a n } = 2 n − 1 10 n ; n ∈ N To evaluate limit of { a n } = 2 n − 1 10 n as n → ∞ . lim n → ∞ { a n } = 2 n − 1 10 n ( ∵ ∞ ∞ f o r m ) = lim n → ∞ 2 n ( ln 2 ) 10 n ( ln 10 )

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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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 3.6, Problem 3TF

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Whether the given sequence 1l0,3100,7l000,l510,000,31100,000,631,000,000........ is convergent or divergent.

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Chapter 3.6, Problem 2TF

Chapter 3.6, Problem 4TF

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Chapter 3 Solutions

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Whether the given sequence 1 l 0 , 3 100 , 7 l 000 , l 5 10 , 000 , 31 100 , 000 , 63 1 , 000 , 000 ........ is convergent or divergent.

Solution Summary: The author analyzes whether the given sequence 1mathrml0, if the n t h term of the sequence approaches unique finite, is convergent or

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Whether the given sequence 1l0,3100,7l000,l510,000,31100,000,631,000,000........ is convergent or divergent.

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Chapter 3 Solutions