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.

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

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.

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Good one

How about this

Multiplying a number by 9 and summing its digits will always get you back to 9😶

maths would be more fun if you learn these statements first and then go to the formulas

TIL that the sum of all positive integers can be shown to equal -1/12

how do you even find this out lol
i hate maths

TIL if you shuffle a deck of cards, it’s highly likely that exact order has never existed in the history of the universe.

Fibonacci numbers:
F_0 = 0
F_1 = 1
F_{n+2} = F_n + F_{n+1}

Sum of Fibonacci numbers:
Σ_{i=0}^n F_i = F_{n+2} - 1

It's a well-known identity 😉
https://en.wikipedia.org/wiki/Fibonacci_sequence#Combinatorial_proofs
There are really a lot of identities for this sequence.

This post has 42 likes. Coincidence? I think not

Yup and like fibs, I'm just the sum of my own mistakes. Is that why I feel so recursive ? 🤣

gm vitalik i sent u a based dickbutt as a gift. i hope you enjoy it <3

Again difficult to understand you 😂 😂 😂

0+1+1+2+3+5=12

13-1=12 

Checks out 👍

Totally unrelated but What’d you think of the new Warpcast UI