A Harmonic Number is a mathematical concept that represents the sum of the reciprocals of the first n natural numbers. It is denoted as H_n and can be expressed as H_n = 1 + \frac12 + \frac13 + \ldots + \frac1n . Harmonic numbers grow logarithmically, meaning they increase slowly as n becomes larger. Harmonic numbers have applications in various fields, including number theory, computer science, and combinatorics. They are particularly useful in analyzing algorithms, especially those involving recursive processes or randomized methods, where understanding the average case performance is essential.