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Monotonic Sequence & Eventually Monotonic Sequence Video Lecture | Mathematics for Competitive Exams
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FAQs on Monotonic Sequence & Eventually Monotonic Sequence Video Lecture - Mathematics for Competitive Exams
| 1. What is a monotonic sequence? |  |
Ans. A monotonic sequence is a sequence of numbers that either increases or decreases consistently as we move along the sequence. In other words, it is a sequence that is either entirely non-increasing or non-decreasing.
| 2. What is an eventually monotonic sequence? | |
Ans. An eventually monotonic sequence is a sequence that may not be monotonic initially, but becomes monotonic after a certain point in the sequence. This means that there exists a term in the sequence beyond which all the terms are either non-increasing or non-decreasing.
| 3. How can we determine if a sequence is monotonic? | |
Ans. To determine if a sequence is monotonic, we can observe the signs of the differences between consecutive terms. If the differences are always non-negative or always non-positive, then the sequence is monotonic. If the differences have both positive and negative values, then the sequence is not monotonic.
| 4. What are the properties of a monotonic sequence? | |
Ans. A monotonic sequence has the following properties:
- If the sequence is non-decreasing, it means that each term is greater than or equal to the previous term.
- If the sequence is non-increasing, it means that each term is less than or equal to the previous term.
- A monotonic sequence can have a limit or can diverge to positive or negative infinity.
| 5. How can we determine if a sequence is eventually monotonic? | |
Ans. To determine if a sequence is eventually monotonic, we can check if there exists a term in the sequence beyond which all the terms have the same sign in their differences. If such a term exists, then the sequence is eventually monotonic. If the terms do not have the same sign in their differences, then the sequence is not eventually monotonic.
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Nov 22, 2024 Last updated |
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