I want to understand this connection better.
Although it sounds the most involved, arctan answers the simplest trigonometric question you could ask. “The full moon subtends seven degrees of my vision; so how big is the moon?” The arctan (with radius = distance from Earth to moon) is the answer.
But what does that simple operation have to do with:
- a continuous sum of
- an inversion of
- one more than
- some sequence of numbers
- times themselves?