  Harmonic numbers arise from the truncation of the harmonic series. The
$n^\text{th}$ harmonic number is the sum of the reciprocals of each positive
integer up to $n$. In addition to briefly introducing the properties of
harmonic numbers, we cover harmonic numbers as the summation of integrals that
involve the product of exponential and hyperbolic secant functions. The proof
is relatively simple since it only comprises the Principle of Mathematical
Induction and integration by parts.
