Determine if the series converges or diverges. Use any method, and give a reason for your answer. n-5 Σ M8 n=5 n7" Does the series converge or diverge? Select the correct choice below and, if necessary, fill in the answer box within your choice. 00 Ο A. Because Σ · Σ n-5 n=5 n7" OC. Because ∞ n-5 Ο B. Because Σ -> [ n=5 n7" OD. Since lim OF. Since n=5 n7" ∞ E. Because Σ 8 n→∞ n7" 5 n-5 n-5 n-5 n7" n=5 n7" = = M88 M8 n-5 2 S n=5 n=5 M8 1 -|C Σ n=5 n 1 n and ∞ and converges, the series converges by the Direct Comparison Test. 1 n=57" Σ · and Σ n=5 n=5 ∞ |- 1 n n=5 1 n the given series diverges by the nth-Term Test for Divergence. diverges, the series diverges by the Direct Comparison Test. 1 converges, the series converges by the Direct Comparison Test. ∞ 1 1 · and Σ diverges, the series diverges by the Direct Comparison Test. 77 n=5 the given series diverges by the Integral Test.
Determine if the series converges or diverges. Use any method, and give a reason for your answer. n-5 Σ M8 n=5 n7" Does the series converge or diverge? Select the correct choice below and, if necessary, fill in the answer box within your choice. 00 Ο A. Because Σ · Σ n-5 n=5 n7" OC. Because ∞ n-5 Ο B. Because Σ -> [ n=5 n7" OD. Since lim OF. Since n=5 n7" ∞ E. Because Σ 8 n→∞ n7" 5 n-5 n-5 n-5 n7" n=5 n7" = = M88 M8 n-5 2 S n=5 n=5 M8 1 -|C Σ n=5 n 1 n and ∞ and converges, the series converges by the Direct Comparison Test. 1 n=57" Σ · and Σ n=5 n=5 ∞ |- 1 n n=5 1 n the given series diverges by the nth-Term Test for Divergence. diverges, the series diverges by the Direct Comparison Test. 1 converges, the series converges by the Direct Comparison Test. ∞ 1 1 · and Σ diverges, the series diverges by the Direct Comparison Test. 77 n=5 the given series diverges by the Integral Test.
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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![Determine if the series converges or diverges. Use any method, and give a reason for your answer.
\[
\sum_{n=5}^{\infty} \frac{n-5}{n7^n}
\]
---
Does the series converge or diverge? Select the correct choice below and, if necessary, fill in the answer box within your choice.
- ○ A. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \leq \sum_{n=5}^{\infty} \frac{1}{n} \) and \(\sum_{n=5}^{\infty} \frac{1}{n} \) converges, the series converges by the Direct Comparison Test.
- ○ B. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \geq \sum_{n=5}^{\infty} \frac{1}{n} \) and \(\sum_{n=5}^{\infty} \frac{1}{n} \) diverges, the series diverges by the Direct Comparison Test.
- ○ C. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \leq \sum_{n=5}^{\infty} \frac{1}{7^n} \) and \(\sum_{n=5}^{\infty} \frac{1}{7^n} \) converges, the series converges by the Direct Comparison Test.
- ○ D. Since \(\lim_{{n \to \infty}} \frac{n-5}{n7^n} = \, \text{[ ]} \), the given series diverges by the nth-Term Test for Divergence.
- ○ E. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \geq \sum_{n=5}^{\infty} \frac{1}{7^n} \) and \(\sum_{n=5}^{\infty} \frac{1}{7^n} \) diverges, the series diverges by the Direct Comparison Test.
- ○ F. Since \(\int_{5}^{\in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf00542e-b5b8-4896-9f9f-a2b46551c658%2F9e675487-1733-484d-a625-8568d972fdc0%2F5mi9wem_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine if the series converges or diverges. Use any method, and give a reason for your answer.
\[
\sum_{n=5}^{\infty} \frac{n-5}{n7^n}
\]
---
Does the series converge or diverge? Select the correct choice below and, if necessary, fill in the answer box within your choice.
- ○ A. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \leq \sum_{n=5}^{\infty} \frac{1}{n} \) and \(\sum_{n=5}^{\infty} \frac{1}{n} \) converges, the series converges by the Direct Comparison Test.
- ○ B. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \geq \sum_{n=5}^{\infty} \frac{1}{n} \) and \(\sum_{n=5}^{\infty} \frac{1}{n} \) diverges, the series diverges by the Direct Comparison Test.
- ○ C. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \leq \sum_{n=5}^{\infty} \frac{1}{7^n} \) and \(\sum_{n=5}^{\infty} \frac{1}{7^n} \) converges, the series converges by the Direct Comparison Test.
- ○ D. Since \(\lim_{{n \to \infty}} \frac{n-5}{n7^n} = \, \text{[ ]} \), the given series diverges by the nth-Term Test for Divergence.
- ○ E. Because \(\sum_{n=5}^{\infty} \frac{n-5}{n7^n} \geq \sum_{n=5}^{\infty} \frac{1}{7^n} \) and \(\sum_{n=5}^{\infty} \frac{1}{7^n} \) diverges, the series diverges by the Direct Comparison Test.
- ○ F. Since \(\int_{5}^{\in
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