## Ramanujan Summation of the Ln(n) Series

**Authors:** Jesús Sánchez

In this paper it will calculated that the Ramanujan summation of the Ln(n) series is:
lim┬█(n→∞)(Ln(1)+Ln(2)+Ln(3)+⋯Ln(n))=Ln(-γ)=Ln(γ)+(2k+1)πi
Being γ the Euler-Mascheroni constant 0.577215... The solution is valid for every integer number k (it has infinite solutions). The series are divergent because Ln(n) tends to infinity as n tends to infinity. But, as in other divergent series, a summation value can be associated to it, using different methods (Cesàro, Abel or Ramanujan).
If we take the logarithm of the absolute value (this is, we take only the real part of the solution), the value corresponds to the smooth continuation to the y axis of the curve that calculates the partial sums at every point, as we will see in the paper.
lim┬█(n→∞)(Ln|1|+Ln|2|+Ln|3|+⋯Ln|n|)=Ln|-γ|=Ln|γ|

**Comments:** 9 Pages.

**Download:** **PDF**

### Submission history

[v1] 2019-01-20 04:27:04

**Unique-IP document downloads:** 58 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.*

*
*