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## Homework Statement

To rephrase the question, given a power series representation for a function, like e

^{x}, and its MacLaurin Series, when I expand the two there's no difference between the two, but my question is: Is this true for all functions? Or does the Radius of Convergence have to do with anything?

On many questions in my Calculus course I am asked to find MacLaurin Polynomial for certain functions, so I don't understand why I should go to all the trouble and find their derivatives and use the definition of a Taylor/MacLaurin Series to find the MacLaurin/Taylor Polynomial, when I can just manipulate the power series and smack down the Nth amount of terms from the power series representation.