I have already asked this question twice & I'm getting the right answer, but I still cannot understand how to get it. This chapter is over the ratio and roots tests. When I have gotten this answered the test that was used was limit comparison. Is there a way to do this equation using the root or ratio test? Again, I understand that the answer is that this series converges conditionally, but I'm really stuck on how to solve using the correct tests, but I didn't specify that before so it's my bad. Thanks so much for your help! **Problem Statement:**Determine whether the given series converges absolutely, converges conditionally, or diverges.\[\sum_{k=1}^{\infty} (-1)^k \frac{k^2 + 5}{4k^3 - 3}\]**Options:**- Converges absolutely- Converges conditionally (Selected option)- DivergesIn this problem, you are asked to analyze an infinite series defined by alternating terms. The series involves a rational expression with polynomials in the numerator and denominator. The task is to determine the nature of its convergence. The selected answer indicates that the series converges conditionally.

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Answered: Determine whether the given series…

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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I have already asked this question twice & I'm getting the right answer, but I still cannot understand how to get it. This chapter is over the ratio and roots tests. When I have gotten this answered the test that was used was limit comparison. Is there a way to do this equation using the root or ratio test? Again, I understand that the answer is that this series converges conditionally, but I'm really stuck on how to solve using the correct tests, but I didn't specify that before so it's my bad. Thanks so much for your help!

**Problem Statement:**

Determine whether the given series converges absolutely, converges conditionally, or diverges.

\[
\sum_{k=1}^{\infty} (-1)^k \frac{k^2 + 5}{4k^3 - 3}
\]

**Options:**

- Converges absolutely
- Converges conditionally (Selected option)
- Diverges

In this problem, you are asked to analyze an infinite series defined by alternating terms. The series involves a rational expression with polynomials in the numerator and denominator. The task is to determine the nature of its convergence. The selected answer indicates that the series converges conditionally.

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