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 […]
Understanding the Integral Test for Series Convergence
TL;DR: When a series looks like a friendly continuous function in disguise, the integral test is your shortcut. If f of x is positive, continuous, and decreasing on the interval from 1 to infinity, then the sum of f of n and the improper integral of f of x will either both converge or both […]
