Example of Divergent Series - Expii

What happens if you try to evaluate a geometric series for a geometric sequence with common ratio greater or equal to 1? How about an infinite arithmetic series like 1+2+3+4+...? There's more to these questions than meets the eye (the most satisfying answers go beyond Algebra 2), but basically we call them "divergent" if it doesn't make sense to assign the sum a value without controversy.