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3. Find the interval of convergence of the power series. Be sure to check for convergence at the endpoints of the intervals. a. b. C. n=0 n=0 n (-1)"n!(x-4)" 3" n(-2x)"-¹ n+1 (-3)"xn n√n n=1 d. En=1

3. Find the interval of convergence of the power series. Be sure to check for convergence at the endpoints of the intervals. a. b. C. n=0 n=0 n (-1)"n!(x-4)" 3" n(-2x)"-¹ n+1 (-3)"xn n√n n=1 d. En=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Power Series Convergence Exercise** **Problem 3:** Find the interval of convergence of the power series. Be sure to check for convergence at the endpoints of the intervals. a. \(\sum_{n=0}^{\infty} \left(\frac{x}{2}\right)^n\) b. \(\sum_{n=0}^{\infty} \frac{(-1)^n n! (x-4)^n}{3^n}\) c. \(\sum_{n=1}^{\infty} n(-2x)^{n-1}\) d. \(\sum_{n=1}^{\infty} \frac{(-3)^n x^n}{n \sqrt{n}}\) **Instructions:** - Determine the interval of convergence for each given power series. - Investigate and confirm convergence at each endpoint within the identified intervals.
Transcribed Image Text:**Power Series Convergence Exercise** **Problem 3:** Find the interval of convergence of the power series. Be sure to check for convergence at the endpoints of the intervals. a. \(\sum_{n=0}^{\infty} \left(\frac{x}{2}\right)^n\) b. \(\sum_{n=0}^{\infty} \frac{(-1)^n n! (x-4)^n}{3^n}\) c. \(\sum_{n=1}^{\infty} n(-2x)^{n-1}\) d. \(\sum_{n=1}^{\infty} \frac{(-3)^n x^n}{n \sqrt{n}}\) **Instructions:** - Determine the interval of convergence for each given power series. - Investigate and confirm convergence at each endpoint within the identified intervals.
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