Harmonic Series

The harmonic series is a sequence of numbers formed by adding together the reciprocals of natural numbers: 1 + 1/2 + 1/3 + 1/4 + ... and so on. Although the terms become smaller, the total sum continues to grow without limit, meaning it diverges. This concept is important in mathematics and physics because it helps describe wave behaviors, sound vibrations, and phenomena where successive contributions decrease but still accumulate significantly over time. The harmonic series illustrates that even diminishing factors can combine to produce an unbounded total.