Answered: Assume you have given a sequence c,,…

Assume you have given a sequence c,, with non-zero values (cn #0 for n = 1,2,...) that fulfils the condition Cn ≤9 Cn-1 for all n = 1,2,3,... for some fixed constant q with 0

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

Assume you have given a sequence c, with non-zero values (cn #0 for n = 1,2,...) that fulfils
the condition
Cn
≤9
Cn-1
for all n 1,2,3,... for some fixed constant q with 0 <q < 1.
=
(a) Show that c₁0 for no. (Hint: use the squeeze theorem)
2"
(b) Use the result from part(a) to show that lim 0
n-x n!
(b) Again: use the result from part(a) to show that lim
1
n-x 3n³
0

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can you explain step 2 and 3 further? like how did you get 2/3 in step 2 and why its n>=3 in step 2?

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