The Integral Test + Example on Convergence of a Series

In this video, I go over the Integral Test, which states that a series converges only if its corresponding improper integral also converges. Likewise, if the improper integral diverges, then the series also diverges. This stems from my earlier introduction video illustrating how the sum of an infinite series is directly tied to the area under the curve of the equation for the terms of the series. I illustrate this with an example on the series with terms 1/(n²+1), which converges since its improper integral converges and equals π/4.

#math #calculus #series #integral #trigonometry