The only way to reason about this is as a limit. lim n->infty sum(1..n)/n. This limit diverges. Your intuition is breaking down. It might be useful for your u

The only way to reason about this is as a limit. lim n->infty sum(1..n)/n. This limit diverges. Your intuition is breaking down. It might be useful for your understanding to study real analysis where these sorts of questions are handled rigorously.