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1.
I have a method to express numbers of the form a/(a^2+1) as continuous fractions. Is there a method to express these numbers as a ratio of two converging sequences such as that a/(a^2+1)≈Kn/Mn?
• CommentAuthorvoloch
• CommentTimeOct 30th 2011

1. You say you have a method. You don't say anything about your method. Is it relevant to the rest of the question?

2. What is "a"? Is it an integer, rational number, real or something else altogether?

3. Continued fraction (not continuous fraction). I kept reading this as continuous function and it made even less sense.

4. Now we get to the real question. We still need an answer to 2. above. What restrictions are you imposing on Kn, Mn? Your oblique reference to continued fractions (but see 3.) makes me think you want them to be integers, but then they can't be convergent, unless constant. So maybe they are not integers, so what are they? What do you mean by a method? What's wrong with a constant sequence?

5. Why should we care? What is the purpose of this question.

It seems to me that you have obtained some results on your own and want to see how interesting/hard/whatever they are. Asking cryptic questions on MO is not the way to find out. MO has a very specific purpose, explained in the FAQ.
• CommentAuthorHenry Cohn
• CommentTimeOct 30th 2011

Regarding expressing a/(a^2+1) as a continued fraction, its simple continued fraction expansion is [0,a,a] (if a is a natural number). Is that what you mean? There are other continued fraction expansions for it, but it is not clear that they are interesting or important.

In any case, I agree with Felipe that as stated this isn't a clear or well motivated question.
2.
Thank you voloch for the comments.
3.
How do I now withdraw this question?
4.