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5. (a) an n→∞ an+1 8 convergence of the power series anx". Show that if lim ii. 8W18W 18 n=0 (b) Using part (a) or the original definition, find the radius of convergence of the following power series. Justify your answer. i. (n!) ² Σ x". (2n)! xn log n =2 - R exists, then R is the radius of

5. (a) an n→∞ an+1 8 convergence of the power series anx". Show that if lim ii. 8W18W 18 n=0 (b) Using part (a) or the original definition, find the radius of convergence of the following power series. Justify your answer. i. (n!) ² Σ x". (2n)! xn log n =2 - R exists, then R is the radius of

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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5. (a) convergence of the power series ii. Show that if lim iii. iMiMiM8 An n→∞ an+1 8 (b) Using part (a) or the original definition, find the radius of convergence of the following power series. Justify your answer. i. (n!) ² (2n)! xn log n -x”. an" where An -- {t n=0 = R exists, then R is the radius of Anxn. 1, if n k² for some ne kEN = 0, otherwise.
Transcribed Image Text:5. (a) convergence of the power series ii. Show that if lim iii. iMiMiM8 An n→∞ an+1 8 (b) Using part (a) or the original definition, find the radius of convergence of the following power series. Justify your answer. i. (n!) ² (2n)! xn log n -x”. an" where An -- {t n=0 = R exists, then R is the radius of Anxn. 1, if n k² for some ne kEN = 0, otherwise.
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