r's = sri, for all 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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can you help me with attached modern algebra question proof by induction
It's number 6 that I need help with
![r's = sri, for all 0 <isn. [Proceed by induction on i and use the fact that
ri+ls = r(r's) together with the preceding calculation.] This indicates how to
commute s with powers of r.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0548f28d-2867-4ce8-91e2-809a65372be3%2F2aca4595-98c8-4328-8f85-727a4a45ec1b%2F025iaps.png&w=3840&q=75)
Transcribed Image Text:r's = sri, for all 0 <isn. [Proceed by induction on i and use the fact that
ri+ls = r(r's) together with the preceding calculation.] This indicates how to
commute s with powers of r.
%3D
Expert Solution
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Step 1
(6) We have to prove that for all using induction on .
When the value , we have and .
Thus, when .
When the value , we have and .
From part (5), we have .
Thus, when .
Thus, the given result is verified for and .
Next, assume the result for .
That is, .
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