Help with the following question The second photo is the rest of the multiple choice **Determine whether the following series converges. Justify your answer.**\[\sum_{k=1}^{\infty} \frac{8^k + 10}{8^k}\]---**Options:**- **A.** The series is a geometric series with a common ratio \(\frac{1}{8}\). This is less than 1, so the series converges by the properties of a geometric series. - **B.** Because \(\frac{8^k + 10}{8^k} \leq \frac{8^k}{8^k} = 1\) for any positive integer \(k\) and \(\sum_{k=1}^{\infty} \frac{8^k}{8^k} = \sum_{k=1}^{\infty} \frac{1}{1}\) converges, the given series converges by the Comparison Test. **Transcription for Educational Website**---**Options for Series Convergence Analysis****C.** Because \[\frac{8}{k} < \frac{8}{k} + \frac{10}{k} \text{ for any positive integer } k \text{ and } \sum \frac{8}{k}\] diverges, the given series diverges by the Comparison Test.**D.** The Ratio Test yields \( r = \_\_\_ \). This is less than 1, so the series converges by the Ratio Test. *(Type an exact answer.)***E.** The series is a geometric series with common ratio \( \_\_\_ \). This is greater than 1, so the series diverges by the properties of a geometric series.**Buttons Below:**- Clear all- Check answer**Note:** This exercise involves applying different convergence tests (Comparison Test, Ratio Test, and properties of geometric series) to determine the behavior of series. Each option outlines a method for assessing divergence or convergence based on mathematical principles. ---This transcription breaks down each option methodically, explaining the reasoning behind the choice of test and the expected outcome regarding series behavior.

Answered: Image /qna-images/answer/2abec71d-1aa2-46da-b3cd-cc6a417cb6cf.jpg

Answered: Determine whether the following series…

Determine whether the following series converges. Justify your answer. 8 + 10 Σ 8 k=1 k

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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