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Example. For n > 1, let sn= series. Σ. The series k km1 Claim. The harmonic series diverges. is called the harmonic k

Example. For n > 1, let sn= series. Σ. The series k km1 Claim. The harmonic series diverges. is called the harmonic k

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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Show that (sn) is not Cauchy. Consider $2n+1-S2n. We have |S2n+1 $2n = - 2+1 1 Σ>2. k k=2"+1 1 2n+1 So (sn) is not Cauchy, so (sn) does not converge. 1 2
Transcribed Image Text:Show that (sn) is not Cauchy. Consider $2n+1-S2n. We have |S2n+1 $2n = - 2+1 1 Σ>2. k k=2"+1 1 2n+1 So (sn) is not Cauchy, so (sn) does not converge. 1 2
Example. For n > 1, let Sn = series. Claim. The harmonic series diverges. Proof. Idea n Σ.. The series k k=1 1+ 2+ 3 V ∞ k is called the harmonic
Transcribed Image Text:Example. For n > 1, let Sn = series. Claim. The harmonic series diverges. Proof. Idea n Σ.. The series k k=1 1+ 2+ 3 V ∞ k is called the harmonic
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