(4) Decide if the following statements are true or false. If true, explain why. If false, give a coun- terexample. (a) If the power series > an(x– n1)" is converges at r = A 1, then it must be convergent at x = 5. :-T n=0 An (b) The power seires > anx" and the power series - x"+1 have the same interval n +1 n=0 n=0 of convergence.
(4) Decide if the following statements are true or false. If true, explain why. If false, give a coun- terexample. (a) If the power series > an(x– n1)" is converges at r = A 1, then it must be convergent at x = 5. :-T n=0 An (b) The power seires > anx" and the power series - x"+1 have the same interval n +1 n=0 n=0 of convergence.
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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Transcribed Image Text:(4) Decide if the following statements are true or false. If true, explain why. If false, give a coun-
terexample.
(a) If the power series > an(x – 1)" is converges at x =
1, then it must be convergent at r = 5.
n=0
An
-xn+1 have the same interval
п+1
n=0
(b) The power seires
Amx" and the power series
n=0
of convergence.
(n!)²
;a". Show your work.
(5) Find the interval of convergence of the power series
(2n)!
n=0
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