Interesting analysis of infinite geometric series

Hello all. My friend and I worked on this paper back in November of last year and completely left it for a while. I am attaching the abstract of the paper below. We'd just like some feedback on the topic and would be happy to provide other parts of it if curious. We are 14 and wish to get feedback on how to go forward with this if possible and that sort of thing so please check the originality as we have some doubts on that front, but be lenient towards us as we were not able to do more than a preliminary check and such, if further inquiry is made. Thank you (no AI btw all written in Overleaf and calculated by us)

https://preview.redd.it/sq0oo1ft7zch1.png?width=1604&format=png&auto=webp&s=7b56a5fccd97c4205986f1be51a56f1e72b98638

Author: mrr934