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Monotonic Sequence - Bounded Sequence Video Lecture | General Aptitude for GATE - Mechanical Engineering
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FAQs on Monotonic Sequence - Bounded Sequence Video Lecture - General Aptitude for GATE - Mechanical Engineering
| 1. What is a monotonic sequence? |  |
Ans. A monotonic sequence is a sequence of numbers that either consistently increases or consistently decreases as the sequence progresses.
| 2. Can a monotonic sequence be bounded? | |
Ans. Yes, a monotonic sequence can be bounded. For example, a sequence that is strictly increasing but bounded above or strictly decreasing but bounded below would be considered a bounded monotonic sequence.
| 3. How can you determine if a sequence is monotonic? | |
Ans. To determine if a sequence is monotonic, you can check if each term is either greater than or equal to the previous term (for a non-decreasing sequence) or less than or equal to the previous term (for a non-increasing sequence).
| 4. What are the characteristics of a bounded sequence? | |
Ans. A bounded sequence is a sequence in which all the terms are within a certain range, either above and below a specific value (bounded) or only above or below a certain value (bounded above or bounded below).
| 5. Why are monotonic sequences and bounded sequences important in mathematics? | |
Ans. Monotonic sequences and bounded sequences are important in mathematics because they help in analyzing the behavior and limits of sequences. They also play a crucial role in various mathematical proofs and applications, especially in the study of limits and convergence.
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