UGC NET Exam > UGC NET Videos > Crash Course for UGC NET Economics > Infinite Series | Sequences & Series| How to check the covergence
Infinite Series | Sequences & Series| How to check the covergence Video Lecture | Crash Course for UGC NET Economics
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FAQs on Infinite Series - Sequences & Series- How to check the covergence Video Lecture - Crash Course for UGC NET Economics
| 1. How do you determine the convergence of an infinite series? |  |
Ans. To determine the convergence of an infinite series, you can use various tests such as the ratio test, comparison test, root test, or the integral test. These tests help determine whether the series converges or diverges based on the behavior of the terms in the series.
| 2. What is the ratio test for checking the convergence of an infinite series? | |
Ans. The ratio test is a common method used to check the convergence of an infinite series. It involves taking the limit of the absolute value of the ratio of consecutive terms in the series. If the limit is less than 1, the series converges; if it is greater than 1, the series diverges; and if it equals 1, the test is inconclusive.
| 3. How does the comparison test help in determining the convergence of an infinite series? | |
Ans. The comparison test is used to compare a given series with a known series that converges or diverges. If the terms of the given series are less than or equal to the terms of the known convergent series, and the known series converges, then the given series also converges. If the terms are greater than or equal to the terms of the known divergent series, then the given series diverges.
| 4. What is the root test and how is it used to check the convergence of an infinite series? | |
Ans. The root test is a method used to determine the convergence of an infinite series by taking the nth root of the absolute value of the terms in the series. If the limit of this nth root is less than 1, the series converges; if it is greater than 1, the series diverges; and if it equals 1, the test is inconclusive.
| 5. How can the integral test be applied to check the convergence of an infinite series? | |
Ans. The integral test is a technique that relates the convergence of an infinite series to the convergence of an improper integral. By comparing the terms of the series to a corresponding function and then evaluating the integral of that function, you can determine whether the series converges or diverges based on the convergence of the integral.
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Dec 25, 2024 Last updated |
Video Description: Infinite Series | Sequences & Series| How to check the covergence for UGC NET 2024 is part of Crash Course for UGC NET Economics preparation.
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