1. (Harmonic Series) Show that Σ k=1 k ≥ log n. ΛΙ Deduce that the series does not converge. Hint. Use the esti- mate ΛΙ k k+1 1 dx. 8

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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1. (Harmonic Series) Show that
Σ
k=1
k
≥ log n.
ΛΙ
Deduce that the series does not converge. Hint. Use the esti-
mate
ΛΙ
k
k+1
1
dx.
8
Transcribed Image Text:1. (Harmonic Series) Show that Σ k=1 k ≥ log n. ΛΙ Deduce that the series does not converge. Hint. Use the esti- mate ΛΙ k k+1 1 dx. 8
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