Question

So i have been using the last couple of days, on a question from my teacher. We have a natural number n. If n is even the next number is : \[\frac{n}{2}\] If n is odd the next number is: \[3n+1\]Problem is that every starting number eventually reaches 1. How would I show that?

Answer 1

I't always reaches the cycle 4,2,1 at some point, at least for the numbers I have tested. It varies how long it takes to reach the cycle.

Answer 2

I saw a video on this, want the link?

Answer 3

Sure

Answer 4

https://www.youtube.com/watch?v=K0yMyUn--0s