Answered: Use the Weierstrass M-test to establish…

Use the Weierstrass M-test to establish the uniform convergence of the following series in the indicated regions. State the convergent series of constants that is employed. ( a) (-2)" for |z|

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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Question

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Use the Weierstrass M-test to establish the uniform convergence of the following series in the indicated
regions. State the convergent series of constants that is employed.
(»)
(-2)" for |z| <r, where r < 1. [Hint: Consider a convergent geometric series of constants]
n+1
(b)
for |2 <r, where r< oo. [Hint: Consider the series for e", where r is real.]
T=1
(c)
for |z| < 1.
n=1

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