# Generalized Harmonic Progression Part II

## TL;DR

This paper extends formulas for summing harmonic progressions of order k by removing integer restrictions on parameters, broadening their applicability with minimal modifications to previous methods.

## Contribution

It generalizes harmonic progression sum formulas to non-integer parameters, enhancing their mathematical scope beyond prior integer-only constraints.

## Key findings

- Derived generalized sum formulas for harmonic progressions with real parameters.
- Identified conditions under which the formulas do not hold.
- Provided a modified derivation approach for the generalized formulas.

## Abstract

In a previous paper, we saw how to create formulae for the sum of the terms of a harmonic progression of order $k$, $HP_k(n)$, with integer parameters, $a$ and $b$. In this new paper we make those formulae more general by lifting the restriction that the parameters be integers. These new formulae always hold, except when $i b/a\in \mathbb{Z}$. This paper employs a slightly modified version of the reasoning used previously. Nonetheless, we make another brief exposition of the principle used to derive them.