Sequences and Limiting Processes
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Alternating (or oscillating) sequence
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A sequence that does not tend to a limit, or does not tend to [Equation] is said to be an alternating (or oscillating) sequence. If an oscillating sequence is bounded it is said to oscillate finitely; otherwise, it oscillates infinitely. Examples 1. Converges to a limit [Equation] 2. Divergent, tends to [Equation][Equation] 3. Divergent, tends to [Equation] [Equation] 4. Oscillates finitely [Equation] 5. Oscillates infinitely [Equation]
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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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