## Approximation of Sum of Harmonic Progression

**Authors:** Aryan Phadke

Background : Sum of Harmonic Progression is an old problem. While a few complex approximations have surfaced, a simple and efficient formula hasn't. Most of the previous formulas use summation as a tool for the approximation. Also, most notable formulas are only applicable to the harmonic progression where the first term and common difference of the corresponding Arithmetic progression is one.
Aim of this paper is to create a formula without using 'summation' as a tool. On the contrary to previous formulas, the resultant formula is applicable to every harmonic progression regardless of the first term and common difference of its corresponding arithmetic progression.
The resultant formula is applicable for numerical values in a harmonic progression. Algebraic terms in a harmonic progression do not value to any numeric terms and for that reason cannot be accounted for the approximation. The resultant formula has a variability in terms of accuracy and complexity to suit different users with different priorities.
The Formula was obtained by equating the area enclosed in the graph of harmonic progression and area under the curve of equation (y=1/x). The logic being that the harmonic progression is completely inclusive in the function (y=1/x) is used to formulate the answer.

**Comments:** 11 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-05-25 02:34:55

[v2] 2019-11-13 03:34:03

**Unique-IP document downloads:** 100 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*