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"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.

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# Taylor Series Interval of COnvergence and Differention + Integration of it

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