I'm not really sure what further to do with arbitrary series.
Theorem one states that if { } and { } have limits and respectively, then { } has the limit .
Is this better. the basic assumption is that since converges, for some N the sum from n to infinty is less than epsilon. Since is a geometric sum, its sum also converges (although less than 1 is sufficient), and so the product of these two will be less than epsilon as well. Is that kinda sorta right for an undergraduate introduction to complex analysis course?