Theories of Infinite Series

Theories of infinite series explore how adding an endless sequence of numbers can either sum to a finite value or diverge. They analyze conditions under which the sum approaches a specific number, like in geometric series where each term decreases proportionally, or harmonic series where terms decrease too slowly, causing divergence. These theories help mathematicians understand the behavior of infinite processes, enabling precise calculations and applications in science and engineering. In essence, they provide a framework for understanding the sum of infinitely many terms and when such sums make sense mathematically.