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Published byPrimrose Ball Modified over 9 years ago
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In this section, we will introduce the idea of an infinite sequence and what it means to say one converges or diverges.
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For example:
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The index variable can be anything; all mean the same thing. The starting index is insignificant. The first term may be We will be interested in the long–run behavior.
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Determine whether each of the following sequences converge.
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Show that the sequenceconverges to 1.
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Suppose the sequence is nondecreasing and bounded above by A. Then converges to some value ≤ A. Suppose the sequence is nonincreasing and bounded below by B. Then converges to some value ≥ B.
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Consider defined by a 1 = 1 and. Show that converges and the limit is ≤ 4.
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