Do the interval and radius of convergence of a power series change when the series is differentiated or integrated? Explain.
Consider the function ,
which is the derivative of the function
This has the power series representation of the form
This series converges when .
The power series representation of is obtained by differentiating the series term by term.thus we get
This also converges when .
Thus the interval and radius of convergence of a power series does not change on differentiating.
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
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