There’s this curious mathematical constant, known as the Euler-Mascheroni Constant. In brief, consider the sum of the first n reciprocals, 1 + 1/2 + 1/3 + … + 1/n. As n goes to infinity, this approaches ln(n). They get very close, with just a slight offset. And that offset converges as n increases. Thus we have,
Numerically, it has the value
So, I was playing around earlier on Mathematica, as is my wont, and discovered the following curious identity, which I present without proof.
