The Harmonic Series

The Harmonic Series is a mathematical sequence formed by adding fractions in the form of 1/n, where n represents positive integers. For example, it starts as 1 + 1/2 + 1/3 + 1/4 + 1/5, and so on. Despite the terms getting smaller, the sum of the series grows indefinitely. This means it diverges, or approaches infinity, even though each individual fraction gets closer to zero. The harmonic series is significant in mathematics, particularly in understanding concepts of infinity and convergence. It serves as a foundation for various fields, including number theory and analysis.