#3 pleaseim confused on when to use what tests ### Section 8.4: Exercises**1. (a)** What is an alternating series? (b) Under what conditions does an alternating series converge? (c) If these conditions are satisfied, what can you say about the remainder after n terms?**2.** What can you say about the series \( \sum a_n \) in each of the following cases?(a) \( \lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 8 \) (b) \( \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = 0.8 \) (c) \( \lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 1 \)**3-8.** Test the series for convergence or divergence.3. \( 4 - \frac{4}{8} + \frac{4}{9} - \frac{4}{10} + \frac{4}{11} - \cdots \)4. \( 4 + \frac{5}{6} + \frac{7}{9} - \frac{11}{8} + \cdots \)5. \( \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{2n+1} \)6. \( \sum_{n=1}^{\infty} (-1)^n \frac{n}{\sqrt{n^3 + 2}} \)7. \( \sum_{n=1}^{\infty} \frac{(-1)^n (3n - 1)}{2n + 1} \)8. \( \sum_{n=1}^{\infty} (-1)^n \cos\left(\frac{\pi}{n}\right) \)**9-12.** Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?---These exercises focus on alternating series, convergence tests, and series evaluation. They require an understanding of limit behaviors, ratio tests, and conditions for convergence.

3. The given series is 47-48+49-410+411-....... We have to find the series is convergence or…

Answered: 3-8 Test the series for convergence or…

3-8 Test the series for convergence or divergence. dhe tadt Hour 3.- + - + 1

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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