math

TIL the sum of all fibs is the second-next fib minus one.

Kinda obvious once you think about it, but still... never seen this mentioned before.

I'd love to see this proof. Typically in math physics a lot of these proofs end up being totally wrong because they're assuming you can do things like distribute across an infinite series.

I would be shocked if this was actually analytically correct.

Proof by induction:

Base case: 1 = 2 - 1
Inductive case: if sum(fib[1...n]) = fib[n+2] - 1, then sum(fib[1...n+1]) = fib[n+1] + fib[n + 2] - 1 = fib[n + 3] - 1

On a more intuitive level, all exponentially growing sequences have a relationship between all terms up to a certain point and a single term beyond that point

What happens as soon as we reach that point?