Maclaurin series similar to those of e^x

I fucking suck at math, but I love it. I genuinely wish I had the time to understand it as profoundly as you.

Edit: I'm very curious about math and fuck with numbers in my free time but its not nearly as complex as what you post. A year or so ago I found something cool, I can't remember exactly how/what I was doing but the result would look like something similar: 0.845749350254069765210543.... (infinitely)

So at first glance it just looks like a huge fucking decimal but if you count the numbers between the zeros, they are the same as the number that immediately proceeds the zero (including the first 0 before the decimal point)

0.845749350

I wish I could remember what I was doing, I have it in a notebook somewhere but since I've moved who knows where that's at