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Monotonic Sequence & Eventually Monotonic Sequence Video Lecture | Mathematics for Competitive Exams

Q: 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.

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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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