s shown in the required reading or videos ove that the harmonic series below diverges ithout using the integral or ratio test, but only = a comparison test. Σ/1/2 n n=1 8
s shown in the required reading or videos ove that the harmonic series below diverges ithout using the integral or ratio test, but only = a comparison test. Σ/1/2 n n=1 8
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Proving the Divergence of the Harmonic Series Using a Comparison Test
As shown in the required reading or videos, prove that the harmonic series below diverges without using the integral or ratio test, but only by a comparison test.
\[ \sum_{n=1}^{\infty} \frac{1}{n} \]
The harmonic series is represented by the summation symbol \(\sum\) from \(n=1\) to \(\infty\), and the general term is the reciprocal of \(n\), \(\frac{1}{n}\).
To prove divergence using a comparison test, follow the method outlined in the coursework. You can consider comparing the harmonic series to a known divergent series or use the Cauchy's Condensation test, which involves comparing the series to a simpler series whose divergence or convergence is established.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42eb3f21-115e-47f2-b59c-753292f0c3d6%2Fc36cb6b1-123c-4d92-ae13-5f42b4722dc7%2F4ngknhf_processed.png&w=3840&q=75)
Transcribed Image Text:### Proving the Divergence of the Harmonic Series Using a Comparison Test
As shown in the required reading or videos, prove that the harmonic series below diverges without using the integral or ratio test, but only by a comparison test.
\[ \sum_{n=1}^{\infty} \frac{1}{n} \]
The harmonic series is represented by the summation symbol \(\sum\) from \(n=1\) to \(\infty\), and the general term is the reciprocal of \(n\), \(\frac{1}{n}\).
To prove divergence using a comparison test, follow the method outlined in the coursework. You can consider comparing the harmonic series to a known divergent series or use the Cauchy's Condensation test, which involves comparing the series to a simpler series whose divergence or convergence is established.
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