Understanding the Integral Test for Series Convergence
The Integral Test is a powerful method for determining the convergence or divergence of an infinite series. It compares the series to an improper integral of a related function. For a series \(\sum a_n\), if \(f(x)\) is a continuous, positive, decreasing function where \(a_n = f(n)\), the convergence of the integral \(\ \int_1^\infty f(x) \, […]
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 […]