True or False? In the following exercises, justify your answer with a proof or a counterexample.
253. If the radius of convergence for a power series
To check: The given statement whether it is true or false and also justified it.
Answer to Problem 253RE
The statement is true.
Explanation of Solution
Given information:
The given statement is:
The radius of convergence for a power series
Concept used:
The radius of convergence R for a power series
Calculation:
The radius of convergence for a power series
Now, the radius of convergence for the series
Therefore, the radius of convergence for the series
Conclusion:
Hence, the given statement is true.
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