Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Convergent, Divergent and Oscillatory Sequence
Convergent, Divergent and Oscillatory Sequence Video Lecture | Mathematics for Competitive Exams
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FAQs on Convergent, Divergent and Oscillatory Sequence Video Lecture - Mathematics for Competitive Exams
| 1. What is the difference between a convergent and a divergent sequence? |  |
Ans. A convergent sequence is a sequence of numbers that approaches a specific limit as the terms go to infinity. In other words, as the terms of the sequence get larger, they get closer and closer to a particular value. On the other hand, a divergent sequence is a sequence of numbers that does not have a limit or approaches infinity. The terms of a divergent sequence do not approach a specific value but become increasingly larger or smaller.
| 2. How can we determine whether a sequence is convergent or divergent? | |
Ans. To determine whether a sequence is convergent or divergent, we can use several methods. One common method is to find the limit of the sequence. If the terms of the sequence approach a specific value as the terms go to infinity, then the sequence is convergent. Another method is to check the behavior of the terms. If the terms of the sequence become increasingly larger or smaller, the sequence is divergent.
| 3. What is an oscillatory sequence? | |
Ans. An oscillatory sequence is a sequence of numbers that does not have a limit but instead fluctuates between two or more values. The terms of an oscillatory sequence do not approach a specific value as the terms go to infinity. Instead, they alternate between increasing and decreasing values, creating a pattern of oscillation.
| 4. How can we identify an oscillatory sequence? | |
Ans. To identify an oscillatory sequence, we need to observe the terms and look for a pattern of oscillation. The terms should alternate between increasing and decreasing values, without approaching a specific value as the terms go to infinity. If the terms fluctuate between two or more distinct values, then the sequence is oscillatory.
| 5. Can a sequence be both convergent and oscillatory? | |
Ans. No, a sequence cannot be both convergent and oscillatory. A convergent sequence approaches a specific limit as the terms go to infinity, while an oscillatory sequence does not have a limit and instead fluctuates between two or more values. These two properties are mutually exclusive, and a sequence can only exhibit one of them.
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Nov 22, 2024 Last updated |
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