Kashyap, Ravi2026-10-122026-10-122026Kashyap, R. (2026). A Lone Ranger, Two Smoking Barrels and the Dirty Dozen: Confirming the harmonious nature (convergence) of the alternating harmonic series and some serious series stuff. Mathematics Teaching-Research Journal, 18(4), 123-183.https://hdl.handle.net/10289/18700This study provides a proof of the convergence of the alternating harmonic series. The alternating harmonic series could be termed the more harmonious sibling of the harmonic series, which is divergent. As a byproduct of this proof - and the associated technique - we arrive at the convergence of a few other series and related results. All the main results are stated as propositions and corollaries, complete with proofs that are simple yet formal. In addition, we create a custom program - code - to numerically illustrate the convergence of one of the series. This serves as an example of how to approach series calculations using computational tools. We verify the convergence of all the series using mathematical software. Our findings confirm the convergence of the alternating harmonic series and several related series. To complement the mathematical content, we have given a compilation of several techniques that can aid in disseminating this knowledge across appropriate audiences. We discuss challenges with respect to mathematics education and provide some pedagogical prescriptions - for the classroom, or other educational settings - to approach the topics we have presented. Our suggestions can help ease the anxiety of participants - who tend to get uneasy when engaging with mathematical material - while performing symbolic manipulations. Despite the simplicity of our proofs - and our belief that these results are surely known - we were surprised that we could not find these results easily elsewhere. This indicates that an unintended consequence of the many advances in mathematics - and related knowledge creation - might be that some knowledge could either be getting lost or just becoming harder to find, which is the equivalent of getting lost in many cases. We outline a potential solution to mitigate this unwanted outcome.enAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/harmonicalternatingBaselconundrumconvergencedivergencefoundharmonicharmoniousillustrationLone RangerlostnumericalproblemseriesThe Dirty DozenTwo Smoking Barrelsunintended consequenceπJournal Article2573-4377