Throwing dice with an infinite number of sides

You have a die with an infinite number of equiprobable sides. Each side is assigned a value: 1,2,3,4… and so on

What are the chanses of you rolling ”a one” at least once if you try an infinite number of times?

The answer is that you have an approximate chance of 63.2% of doing that.

There is that number again, 63.2 !

The exact answer is

Some people may find that a trivial problem, but I think it’s interesting. I have never seen it expressed before.

That number is also at the root of my Hithchikers-Guide-Encoded-in-Pi problem and the Bonds Integer from my last post.