Convergence tests are mathematical methods used to determine whether a series or sequence converges, meaning it approaches a specific value as more terms are added. These tests help identify if the sum of an infinite series will yield a finite result or diverge to infinity. Common tests include the Ratio Test, Root Test, and Comparison Test. These tests are essential in calculus and analysis, providing tools for mathematicians and scientists to evaluate the behavior of series. By applying these tests, one can simplify complex problems and gain insights into the properties of functions and sequences in various applications.