(b) Prove that the real power series n!r" converges for only r 0. %3D
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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this is math
![(3) As a preparation for what we'll do next week, read over your old calculus
text about infinite series and power series.
(a) Prove that the real power series
(-1)"z2"
converges for every real
n!
r.
(b) Prove that the real power series n!r" converges for only a = 0.
(c) Pick your favourite real power series a,a". Show that for this
series, the equivalence
%3D
30
Σ
ana" converges +
>
na,r"- converges.
n=0
holds, with the possible exception of at most two real values of a,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4703214b-7b6d-48dc-8fec-73bc2badaa48%2F00b672c0-698d-4da5-81d7-050b9e4dfb05%2Fmestssd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(3) As a preparation for what we'll do next week, read over your old calculus
text about infinite series and power series.
(a) Prove that the real power series
(-1)"z2"
converges for every real
n!
r.
(b) Prove that the real power series n!r" converges for only a = 0.
(c) Pick your favourite real power series a,a". Show that for this
series, the equivalence
%3D
30
Σ
ana" converges +
>
na,r"- converges.
n=0
holds, with the possible exception of at most two real values of a,
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