Sequences and Limiting Processes
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Limits
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In a null sequence the terms approach zero as n tends to infinity. We write this [Equation goes here - download the original to see it.] or [Equation goes here - download the original to see it.] Sequences may tend to values other than zero. In such a case the sequence is said to approach a limit. Definition: A sequence [Equation] is said to tend to the limit l if, for any positive number [Equation], there exists an N depending on such that [Equation] This is written [Equation] Remarks 1. [Equation]. 2. [Equation] means [Equation] Hence [Equation] is bounded.
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Contents of
Sequences and Limiting Processes
1 Sequences
2 Null sequences
3 Limits
4 Sequences tending to infinity
5 Alternating (or oscillating) sequence
6 Combining limits
7 Monotone sequences
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