OK.... "A power series can be differentiated or integrated term by term over any interval lying entirely within the interval of convergence" When i do term by term differentiaion or t-by-t integration of a series though, am i making use of this fact? Does this come into play later in a class? Or is this fact referring to if i wanted to take the rate of change of the summation, then i can only do it on the interval of convergence. Any response or even just an elaboration would be helpfull. Kind of confused about the matter. Thanks.