Let (n) be a sequence defined by 2₁ = 1 and for n ≥ 2, 1 2+²-1 In Prove that (n) is Cauchy using the definition of Cauchy Sequence and then find its limit. Hint: Show that for all n ≥ 2, one has |£n+1 = £n] < } ]£n − En-1. The triangle inequality and geometric se- ries formula may be useful after this.
Let (n) be a sequence defined by 2₁ = 1 and for n ≥ 2, 1 2+²-1 In Prove that (n) is Cauchy using the definition of Cauchy Sequence and then find its limit. Hint: Show that for all n ≥ 2, one has |£n+1 = £n] < } ]£n − En-1. The triangle inequality and geometric se- ries formula may be useful after this.
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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![Let (n) be a sequence defined by 2₁ = 1 and for n ≥ 2,
1
2+²-1
In
Prove that (n) is Cauchy using the definition of Cauchy Sequence
and then find its limit. Hint: Show that for all n ≥ 2, one has
|£n+1 = £n] < } ]£n − En-1. The triangle inequality and geometric se-
ries formula may be useful after this.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac744b86-fb77-4dc8-9b17-1f74c21e67b7%2Fb9ca852c-b7ec-44e8-8d68-32577e94280d%2Fe9rxpg9_processed.png&w=3840&q=75)
Transcribed Image Text:Let (n) be a sequence defined by 2₁ = 1 and for n ≥ 2,
1
2+²-1
In
Prove that (n) is Cauchy using the definition of Cauchy Sequence
and then find its limit. Hint: Show that for all n ≥ 2, one has
|£n+1 = £n] < } ]£n − En-1. The triangle inequality and geometric se-
ries formula may be useful after this.
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