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Use the divergent test to analyze the given series. Each answer should either be the serie diverges or the divergence test fails, along with the reason for your answer. ∞ k=1 k 3k² + 100

Use the divergent test to analyze the given series. Each answer should either be the serie diverges or the divergence test fails, along with the reason for your answer. ∞ k=1 k 3k² + 100

Calculus: Early Transcendentals
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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Use the divergent test to analyze the given series. Each answer should either be *the series diverges* or *the divergence test fails*, along with the reason for your answer. \[ \sum_{k=1}^{\infty} \frac{k}{3k^2 + 100} \]
Transcribed Image Text:Use the divergent test to analyze the given series. Each answer should either be *the series diverges* or *the divergence test fails*, along with the reason for your answer. \[ \sum_{k=1}^{\infty} \frac{k}{3k^2 + 100} \]
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\sum _{k=1}^{\infty }\:\frac{k}{3k^2+100}

use the series integral test:

if an is positive, continuous, and decreasing then \sum _{n=k}^{\infty }a_n\:\:\:\:\:\mathrm{and}\:\:\:\:\int _k^{\infty }f\left(x\right)dx

either converge or diverge.

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