Through the educational processes of learning mathematical theorems, students can broaden their views by discovering the relationships between different concepts. As a pedagogical example, the recurrence relation between infinite series and generalised harmonic numbers is discussed. A recurrence relation is deduced between the infinite class of convergent series and a family of summations involving generalised harmonic series. Formulae established through the process of derivation are related to the Riemann zeta function and Seki-Bernoulli numbers. Instructors can set the derivation of these formulae as exercise problems in order for students to learn the regularity of these series.

derivative operator, generalised harmonic numbers, infinite series, Riemann zeta function, Seki-Bernoulli numbers.