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

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A user claims to have discovered a formula for the nth term of any finite sequence of numbers but is concerned about its originality and potential publication. The formula presented is criticized for only applying to arithmetic progressions, which are well-known and trivial. Participants argue that no universal formula can predict the next term of a general sequence due to the infinite possibilities of sequences. The discussion reveals that the user's formula resembles polynomial interpolation, specifically Newton's method, which has already been established in mathematics. Ultimately, the user acknowledges that their findings are not new and expresses a desire to understand the implications of their work in relation to existing mathematical principles.
  • #31


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.

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??
 
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  • #32


Vargo said:
finite sequence
No such thing exists.
 
  • #33


johnqwertyful said:
No such thing exists.

While you're formally correct, it's a bit hairsplitting don't you think? We all know what he meant with it and many people do use this term.
 
  • #34


micromass said:
While you're formally correct, it's a bit hairsplitting don't you think? We all know what he meant with it and many people do use this term.

Not at all. I think it's important to use correct terminology; the way things are formally defined in a formal setting.
 
  • #35


johnqwertyful said:
Not at all. I think it's important to use correct terminology; the way things are formally defined in a formal setting.

It is formal. Many good math books use the terminology "finite sequence". For example: "Mathematical analysis" by Apostol, Definition 2.12.
 
  • #36


Or "Real Analysis" by Royden, page 9.

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

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