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Infinite Series - 1 Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
FAQs on Infinite Series - 1 Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is an infinite series? |  |
Ans. An infinite series is a sum of an infinite number of terms. It is denoted by ∑ (sigma) followed by the terms. The terms can be positive, negative, or zero, and they follow a specific pattern or rule.
| 2. How do you determine if an infinite series converges or diverges? | |
Ans. To determine whether an infinite series converges or diverges, we can use various tests such as the divergence test, comparison test, ratio test, or integral test. These tests help us analyze the behavior of the terms in the series and determine if the sum of the terms approaches a finite value (converges) or goes to infinity (diverges).
| 3. What is the difference between a finite series and an infinite series? | |
Ans. A finite series is a sum of a fixed number of terms, while an infinite series has an infinite number of terms. In a finite series, there is a definite end point, whereas an infinite series continues indefinitely. The behavior and properties of finite and infinite series can differ significantly.
| 4. Can an infinite series have a sum if the terms go to zero? | |
Ans. Yes, an infinite series can have a finite sum even if the terms go to zero. This is known as a convergent series. The terms may approach zero at a certain rate or follow a specific pattern that allows the sum to converge to a finite value. However, it is important to note that not all series with terms approaching zero converge.
| 5. What are some real-life applications of infinite series? | |
Ans. Infinite series have various applications in different fields. Some examples include the use of infinite series in calculus to approximate functions, in physics to model physical phenomena, in finance to calculate compound interest, and in computer science for algorithms and simulations. Infinite series provide valuable mathematical tools for analyzing and solving real-world problems.
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