Infinite Series

An infinite series is the sum of infinitely many numbers added together. Imagine adding numbers one after another forever; while it seems it would never end, sometimes these sums approach a specific value, known as a limit. For example, 1/2 + 1/4 + 1/8 + 1/16 + ... adds up very closely to 1. Infinite series are fundamental in mathematics because they help us understand and analyze functions, calculate areas, and model real-world phenomena where processes continue indefinitely. They combine an infinite process with a finite result, revealing patterns and relationships that are key in advanced math.