I have almost no background in mathematics. However, it occurred to me (while doing a poli sci thing) that one could create a sequence of fractions, in which the denominator is the next odd number, and the numerator, the smallest possible numerator that would make the fraction over half. For denominator 1, this would be 1/1, or 100%; for denominator 3, 2/3, or 66.666...%; for denominator 5, 3/5, or 60%, and so on.
When using just odd numbers as the denominator, it seems this sequence approaches 50%. (If one includes even numbers, it doesn't, because for fractions with an even denominator, there is a numerator that makes the fraction exactly half--so the next numerator up would give it more of a 'boost' than when the denominator is odd [e.g., 3/4].)
I was going to use this idea for a non-mathematical application, but I don't know if the above is really a thing. I thought it would be, but googling it didn't bring up anything other than some tutoring site questions (e.g. here), which don't indicate that the sequence has any validity or interest in and of itself.