Solution Found!
Do the interval and radius of convergence of a power
Chapter 8, Problem 5E(choose chapter or problem)
QUESTION:
Do the interval and radius of convergence of a power series change when the series is differentiated or integrated? Explain.
Questions & Answers
QUESTION:
Do the interval and radius of convergence of a power series change when the series is differentiated or integrated? Explain.
ANSWER:Solution 5E
Step 1:
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.