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Definition of the Limit of a Sequence Video Lecture | Mathematics Optional Notes for UPSC

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FAQs on Definition of the Limit of a Sequence Video Lecture - Mathematics Optional Notes for UPSC

1. What is the limit of a sequence?
Ans. The limit of a sequence is a real number towards which the terms of the sequence progressively approach as the sequence goes to infinity.
2. How is the limit of a sequence calculated?
Ans. The limit of a sequence can be calculated by observing the behavior of the terms as n approaches infinity. If the terms get arbitrarily close to a single value as n increases, that value is the limit of the sequence.
3. Can a sequence have more than one limit?
Ans. No, a sequence can only have one limit. If the terms of a sequence approach different values as n approaches infinity, then the sequence is said to diverge and does not have a limit.
4. What is the difference between a convergent and a divergent sequence?
Ans. A convergent sequence has a limit, meaning that its terms approach a single value as n goes to infinity. A divergent sequence does not have a limit, as its terms do not converge to a single value.
5. How is the concept of limit of a sequence important in calculus?
Ans. The concept of the limit of a sequence is foundational in calculus as it forms the basis for understanding the limit of a function. By understanding how sequences behave and converge, one can better comprehend the behavior of functions and their limits.
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