I discovered a formula for the nth term of any sequence of numbers

In summary, the conversation revolved around the discovery of a formula for the nth term of any finite sequence of numbers. The formula provided was for an arithmetic progression and it was mentioned that there cannot be a formula for predicting an element of a general sequence. The original formula proposed was questioned and it was suggested to consider publishing it. However, it was later discovered that a similar formula had already been discovered by a 6-year-old mathematician. The conversation also touched upon the concern of someone stealing the formula and not receiving credit for its discovery.
  • #36


Or "Real Analysis" by Royden, page 9.

I'm sure I can find many others.
 
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  • #38


i don't think so. i have one in mind whose nth term is ?
 
  • #39


Vargo said:
If you carefully read the original post, you would see that there is no intrinsic flaw in his claim. He is not trying to create a nonsense formula for the nth term in a sequence given a list of the first k terms.

Instead he has a finite sequence u_1, ..., u_n. Given those numbers, he finds an explicit polynomial P(n) such that P(i)=u_i. There is no infinite sequence and it has nothing to do with pattern recognition. It is simply a polynomial interpolation and that is all he is claiming.
The formula in the first post is not the one OP had in mind - that was posted later. That didn't help matters.
If the original post were not clear (which is understandable since the OP is not trained in maths), surely some of the follow up posts would have cleared this up??
Yet so many people are responding as if the claim is that the formula is predicting the next term in the intended sequence. Like:
mathwonk said:
i don't think so. i have one in mind whose nth term is ?
... I don't think OP is actually claiming to be able to predict the next term in mathwonk's sequence ... just to be able to come up with "a" next term given what has gone before and the assumptions (reasoning?) built-in to the formula. The formula would be predictive for a particular kind of sequence.

The wording in post #1 is unclear on this point, and muddied, rather than clarified, by crossed wires in later responses, but I think we are at the point where OP can be encouraged to confirm or deny the interpretation unambiguously.

I submit: further discussion is pointless until that happens.
 
  • #40


Simon Bridge said:
The wording in post #1 is unclear on this point, and muddied, rather than clarified, by crossed wires in later responses, but I think we are at the point where OP can be encouraged to confirm or deny the interpretation unambiguously.

I submit: further discussion is pointless until that happens.

He already did so, see the start of post #17. This thread is done, and the original poster said so himself in post #20.
 
  • #41


From post #20:
I didn't understand the formulas on the Wikipedia page that you posted here, but now I do. I see that this discussion could have ended a lot sooner.
... not specific.
The confusion still continued though: witness the remaining posts.

I agree the thread is finished with no further input from OP.
 
  • #42


Locked.
 
<h2>1. How did you come up with the formula?</h2><p>I used a combination of mathematical reasoning and trial and error to derive the formula. It involved analyzing patterns and relationships between the terms in the sequence.</p><h2>2. Can you explain the formula in simple terms?</h2><p>The formula involves using the position of a term in the sequence (represented by 'n') to calculate the value of that term. It may also involve using other terms in the sequence and basic mathematical operations such as addition, subtraction, multiplication, and division.</p><h2>3. Does the formula work for all types of sequences?</h2><p>Yes, the formula is designed to work for any type of sequence of numbers, whether it is arithmetic, geometric, or any other type of sequence. As long as the sequence follows a pattern, the formula can be used to find the value of any term in that sequence.</p><h2>4. Can the formula be used for infinite sequences?</h2><p>Yes, the formula can be used for infinite sequences as long as the pattern or rule of the sequence is known. It can also be used to find the value of terms that are beyond the given sequence, as long as the pattern continues.</p><h2>5. How can the formula be applied in real life?</h2><p>The formula can be applied in various fields such as finance, engineering, and computer science to predict future values or to solve problems involving sequences of numbers. It can also be used to analyze and understand patterns in data sets.</p>

1. How did you come up with the formula?

I used a combination of mathematical reasoning and trial and error to derive the formula. It involved analyzing patterns and relationships between the terms in the sequence.

2. Can you explain the formula in simple terms?

The formula involves using the position of a term in the sequence (represented by 'n') to calculate the value of that term. It may also involve using other terms in the sequence and basic mathematical operations such as addition, subtraction, multiplication, and division.

3. Does the formula work for all types of sequences?

Yes, the formula is designed to work for any type of sequence of numbers, whether it is arithmetic, geometric, or any other type of sequence. As long as the sequence follows a pattern, the formula can be used to find the value of any term in that sequence.

4. Can the formula be used for infinite sequences?

Yes, the formula can be used for infinite sequences as long as the pattern or rule of the sequence is known. It can also be used to find the value of terms that are beyond the given sequence, as long as the pattern continues.

5. How can the formula be applied in real life?

The formula can be applied in various fields such as finance, engineering, and computer science to predict future values or to solve problems involving sequences of numbers. It can also be used to analyze and understand patterns in data sets.

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