Does the following series converge or diverge? Give reasons for your answer. ∞0 I 20" (n!) n=1 (n^) ² Σ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series diverges by the nth-Term Test. OB. The series converges because the limit used in the Root Test is O C. The series diverges because the limit used in the Root Test is O D. The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series converges by the nth-Term Test. <1. >1.
Does the following series converge or diverge? Give reasons for your answer. ∞0 I 20" (n!) n=1 (n^) ² Σ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series diverges by the nth-Term Test. OB. The series converges because the limit used in the Root Test is O C. The series diverges because the limit used in the Root Test is O D. The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series converges by the nth-Term Test. <1. >1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![Does the following series converge or diverge? Give reasons for your answer.
\[
\sum_{n=1}^{\infty} \frac{20^n (n!)^n}{(n^n)^2}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. ⬤ The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series diverges by the nth-Term Test.
B. ⬤ The series converges because the limit used in the Root Test is \([ \, ] < 1\).
C. ⬤ The series diverges because the limit used in the Root Test is \([ \, ] > 1\).
D. ⬤ The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series converges by the nth-Term Test.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf00542e-b5b8-4896-9f9f-a2b46551c658%2F787e0d75-4616-40fe-8693-5fa0f2c47ab1%2F34qcn9q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Does the following series converge or diverge? Give reasons for your answer.
\[
\sum_{n=1}^{\infty} \frac{20^n (n!)^n}{(n^n)^2}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. ⬤ The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series diverges by the nth-Term Test.
B. ⬤ The series converges because the limit used in the Root Test is \([ \, ] < 1\).
C. ⬤ The series diverges because the limit used in the Root Test is \([ \, ] > 1\).
D. ⬤ The Root Test is inconclusive because the limit used in the Root Test is equal to 1, but the series converges by the nth-Term Test.
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