Hızlı yanıt: kod örneği
Essentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature. I.e., since such a definition would be given for the sake of completeness and coherence with the fact "the limiting ratio is the ratio of the limits", your$$ \frac{1 + 1 + \cdots}{2 + 2 + \cdots} = \lim_{n \to \infty} \frac{n}{2n} = \frac{1}{2} $$and, say (this is my choice)$$ \frac{1 + 1 + 1 + \cdots}{1 + 2 + 3 + \cdots} = \lim_{n \to \infty} \frac{n}{n(n+1)/2} = 0 $$would have to be equal (as they commonly define $\infty/\infty$), which does not happen.