Whats the answer to the The Collatz Conjecture

The Collatz conjecture, also known as conjecture , conjecture of Ulam or problem of Syracuse, is a conjecture of number theory established by Lothar Collatz in 1937 and says the following: If is an even number, divide it by 2 until you reach an odd number or 1, if is an odd number different from 1, multiply it by 3 and add 1 and start the process of dividing by 2, the final result will always be 1. The above means that this process always ends when being , because the successive division k times 2 of is 1. Formally, this equates to a function f:N↦N, such that: f(n)= { (n/2, or (3n+1)/2, or n=2^k, or (3n+1)/2=2^k)

I hope it's helpful!

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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for