For what real values of i does the sum of ε^i, taken ε=1 to infinity, converge? Our real analysis lecturer once put this question on the blackboard (with sum a

For what real values of i does the sum of ε^i, taken ε=1 to infinity, converge? Our real analysis lecturer once put this question on the blackboard (with sum as the proper scientific sum notation). Even though we all knew the answer as trivial it took most of us some time to figure it out in such screwy notation (his point was that our mind is not invariant WRT notation, do not make up monsters when the normal schemas exist)