sigh -1/12 Again
So I'm sure most people know about the infamous -1/12 and its connection to 1+2+3+4... and so on. I was watching a numberphile video on the topic and a commenter pointed out something I thought interesting. We all know that (n(n+1))/2 can be used to find the sum of the natural numbers up to n. But as it turns out, the integral from -1 to 0, is also -1/12.
I'm curious if there is any connection there or merely a coincidence. I tried looking it up to see if anyone else has made this connection. Unfortunately, I'm not that well versed in higher math, the most I ever took was business calc so I'm way out of my league here.