Convergence Theorems

Convergence theorems are principles used to determine how a sequence of values approaches a certain point or behavior as it continues indefinitely. In mathematics, they help us understand whether a series of numbers, functions, or sequences settle down to a specific value (the limit) or diverge away from it. For example, if you keep averaging a set of numbers, convergence theorems tell us under what conditions that average will stabilize at a particular value. These concepts are fundamental in fields like calculus and analysis, helping to analyze stability and behavior of mathematical systems.