>>9537979Neither can exceed bounds or else thered be a largest natural number, which is a contradiction to peanos axioms.
It's important to remember the sequence n+1 is a tail of the sequence n.
So what's really being said is if some tail of the sequence (n+1) approaches a value larger than the sequence contained by it (n) then the original sequence diverges, so the sum diverges.
If however, the tail is decreasing, then the sequence (n) converges so its sum converges.
If the sequence is constant, it can converge or diverge. So you don't know if the sum will converge or not.
