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Simplifying fraction with factorials: $\\frac{(3(n+1))!}{(3n)!}$ $$ (3 (n+1))! \neq 3 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 4 \cdots 3 \cdot (n+1) $$ To make it clear what the problem is, let's write the right-hand side with brackets: $$ (3 \cdot 2) \cdot (3 \cdot 3) \cdot (3 \cdot 4) \cdots (3 \cdot (n+1)) $$ That's just multiplying all the positive multiples of 3 less than $ 3 (n+1) $ together; the factorial is defined as multiplying together all positive
combinations - Relation connecting $ (3n)!$, $3^n$ and $n . . . You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
Collatz conjecture but with $\ 3n-1\ $ instead of $\ 3n+1. \ $ Do any . . . Because 3n+1 is the same as the absolute value of 3n-1 for negative numbers So the question remains unanswered If you found "lots" of answers that would be interesting, since I am only aware of 5 total sequences being found in the collatz conjecture, namely 1, 0, -1, -5, -17
What is the importance of the Collatz conjecture? [closed] What delights me most about the Collatz conjecture is your observation about what the iteration does to the factorizations combined with an observation on the sizes of the numbers Multiplication by 3 and adding 1 more than triples the number, while dividing by 2 only halves it If you ended up doing a large number of iterations to compute the sequence, and each was equally likely, then you
Prove $3^n gt; n^2$ by induction - Mathematics Stack Exchange The $3n^2 > (n + 1)^2$ inequality might seem suspicious One way to see that it will be valid for sufficiently large $n$ is to consider the order of growth of both sides of the inequality
How do you make 500ml of 3N NaOH? - Answers Since HCl is a monoprotic acid, its normality is the same as its molarity A 4 N solution of HCl is a 4 M solution of HCl as well If you want to make a liter of a 4 N solution of HCl, you need to