Convergence Tests

Convergence tests are methods used in mathematics to determine whether an infinite series (a sum of infinitely many numbers) has a finite value or not. Think of adding numbers that go on forever; convergence tests help us decide if the total sum settles into a specific number (converges) or keeps growing without bound (diverges). Examples include the comparison test, ratio test, and root test. These tests analyze the behavior of the terms in the series to ensure that the sum approaches a limit, providing a systematic way to confirm the series' convergence or divergence.