Question

4. Determine the radius and interval of convergence of the following power series: (Hint: Remember to check the end points of the intervals of convergence.) (a) ?_{n=1}^{?} (-1)?nx? (b) ?_{n=1}^{?} x? / (n?4?)

          4. Determine the radius and interval of convergence of the following power series:
(Hint: Remember to check the end points of the intervals of convergence.)
(a) ?_{n=1}^{?} (-1)?nx?
(b) ?_{n=1}^{?} x? / (n?4?)

Added by Mary L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

08/18/2023

Step 1

It seems there are some typos in the given series, so I will assume the correct series is: $$\sum_{n=1}^{\infty} (-1)^n 2^n n^{4n} x^n$$ Now, we will use the Ratio Test to find the radius of convergence. The Ratio Test states that if $\lim_{n\to\infty} Show more…

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Determine the radius and interval of convergence of the following power series: (Hint: Remember to check the endpoints of the intervals of convergence:)