If I have a finite sequence of expressions $a_1+a_2+a_3+....a_k=\infty$, does that imply that at least one such $a_j=\infty$?
I know that if it didn't it would make the sum not equal to infinity, but it still does not make intuitive sense to me. Couldn't part of the magnitude be contained in each expression equally and still be such that one term didn't diverge?