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MTH251-Lecture 29 Notes-Power Series

Consider,

We want to represent this as a power series

For

Differentiation and integration of power series

If f(x) has a power series representation

whose domain is the set of a, x

such that the series converges, then we would like to be able to differentiate and integrate f.

The following theorem tells us how

Theorem: Term-by-term differentiation and integration of power series