Series Behavior with the n-th Term Test: Divergence Test
The n-th Term Test is a fundamental tool in determining whether a series converges or diverges. It examines the behavior of the terms in a series as \(n\) approaches infinity. Specifically, if the limit of the n-th term \(a_n\) does not approach zero, the series diverges. However, if \(\lim_{n \to \infty}\) a_\(n = 0\), the […]
Employing the Limit Comparison Test to Analyze Series Convergence
The Limit Comparison Test is a technique used to determine whether a series converges or diverges by comparing it to another series with known behavior. You examine the ratio of the terms of both series as the terms approach infinity. If the ratio approaches a positive, finite number, both series will behave the same in […]