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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

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
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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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
Transcribed Image Text: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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