A Divergent Series is a type of infinite series that does not converge to a finite limit. In simpler terms, as you keep adding more and more terms of the series, the total sum grows indefinitely or oscillates without settling down to a specific value. This behavior is crucial in various fields of mathematics and physics, as it helps in understanding the limits of certain functions and models. One common example of a divergent series is the harmonic series, which is the sum of the reciprocals of the natural numbers. Despite the individual terms getting smaller, the overall sum increases without bound, illustrating the concept of divergence in a clear manner.