Convergent Sequences

A convergent sequence is a series of numbers where the terms get closer and closer to a specific value, called the limit, as the sequence progresses. Imagine steadily approaching a destination; each step gets you nearer to that point. For example, the sequence 1, 0.5, 0.25, 0.125, ... gets closer to zero. Convergence indicates stability in the sequence’s behavior, meaning the numbers eventually settle near a single value, even if they don’t necessarily reach it exactly. This concept is essential in understanding how sequences behave and in various fields like calculus and analysis.