if you have absolutely no grounding in maths or science, then sure, it would be unusual to think that way, but if you do, which you clearly did, then it should

if you have absolutely no grounding in maths or science, then sure, it would be unusual to think that way, but if you do, which you clearly did, then it should no longer be unusual whatsoever. it would be trivial to artificially construct a series that equals 1 until n=10^10 at which point it equals pi/785498. if these series do exist, then - without additional information - why would you ever think that one you're studying is not one of them? even from a metaepistemological standpoint, had you never come across the notion that, for example, Fermat's Last Theorem could not have been proven simply by showing that 10^10/infinity of the possible outcomes had been shown to follow it? >It seems that for such a simple problem, involving basic arithmetic and small numbers, 1, 2, and 3, there should be a number N where if you try all examples less than N, you have sufficient "resolution" to reveal all patterns between the numbers does it? why?