The Harmonic Series: Infinite Growth and Mathematical Impact
The harmonic series is an infinite series formed by the sum of the reciprocals of natural numbers: \(1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \ldots\). Although each term becomes progressively smaller, the series diverges, meaning it grows indefinitely without reaching a finite limit. This surprising result is crucial in mathematical analysis and has applications […]