Cauchy series

A Cauchy series is a mathematical concept describing a sequence of numbers where the terms become arbitrarily close to each other as the sequence progresses. Essentially, as you move further along the series, the difference between any two terms gets smaller and smaller, approaching zero. This property indicates that the series "converges" to a specific value, even if that value isn't immediately obvious. It's an important idea in analysis because it helps mathematicians understand when infinite sums or sequences settle into a predictable value, ensuring their behavior is well-defined and consistent.