When (x+y+z)^2017 is expanded and simplified, how many different terms will there be?
Raise (x+y+z)^2017 and get a giant mess. Then simplify. Then count the terms.
Or find a better way.
Hint: Is there a way to do this with combinations?
This picture makes me think about combinatorics and the multinomial expansion...
Nice question. Would be good to see more of these. Upvoted and followed.
any solution? :)
This essentially boils down to the partitions of 2017 with just 3 terms.
So we are going from x2017y0z0 to x0y0z2017.
So, just looking at the powers:
2017-0-0
2016-1-0
2016-0-1
2015-2-0
2015-1-1
2015-0-2 etc etc....
so we have the sum of integers n(n+1)/2 = 2018x2019/2 = 2037171 (as we start with zero, not1)
That's a great way of doing it. My way of remembering it is, "How many ways can you divide 2017 pieces of candy among 3 children?" Where this is a combination problem. The little tricks are in making sure you choose 1 less arrangement, for example, you only need to choose 2, and you need 2019 items (candy + children - 1). So 2019 choose 2 is also the answer.
Yes, that's the same problem. Just as with the kids and candy, order is important here; the number partition problem can be done as permutations or combinations, depending on the problem.
This is a representation of our holographic universe
Haha, I honestly do not know much about that? Seriously? Can you elaborate please?
I am a research scientist. We live in a holographic plane. This side of counter space (which is where you and I exist) everything breaks down into fractals. Everything exists based on frequency generations within the electromagnetic field that we call the ether. Your diagram shows the mathematical representation of these fractals. We are finding out that most of what we were taught in the universities is not 100% correct. One clue I will give you (that we have discovered) is there are secrets to the water molecule. H2O is the most misunderstood molecular compound on Earth. Water has a unique structure that interacts with counter space!
Hi @jetblake maybe you can write more about your discoveries.
Water is far far weirder than most people can imagine.
I've heard that our reality is created from a binary code. I have also learned that earth is a series of repeating patterns.
I think this supports the Bible because God created by speaking; A word is frequency, vibration and intention of will
Exactly. We have proven in our research that a source or God does exist. This GOD exists outside our reality. It is an inexhaustible energy source that has always existed. It creates a reality through conscious thought/word which as you correctly stated is a frequency vibration. We have also found that our thoughts and behavior can either be in harmony with this SOURCE or not. If you are in harmony than the reality provides positive/joyful experiences. If not in harmony than negative/non joyful experiences. Hope I am making a little sense. LOL
I am also a researcher and this is very new to me:)
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