That is, under what conditions would
$$ \sum_{i = 1}^n \frac{a_i}{b_i}= \frac{\sum_{i = 1}^n a_i}{\sum_{i = 1}^n b_i} $$
be true? What about for infinite summations, i.e. when $n \rightarrow \infty$?
That is, under what conditions would
$$ \sum_{i = 1}^n \frac{a_i}{b_i}= \frac{\sum_{i = 1}^n a_i}{\sum_{i = 1}^n b_i} $$
be true? What about for infinite summations, i.e. when $n \rightarrow \infty$?