Determine whether the sequence converges or diverges. If it converges, find the lin DIVERGES.) 500-n
Determine whether the sequence converges or diverges. If it converges, find the lin DIVERGES.) 500-n
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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![**Problem: Sequence Convergence or Divergence**
Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.)
\[ a_n = 5^n 9^{-n} \]
\[ \lim_{n \rightarrow \infty} a_n = \boxed{} \]
**Instructions:**
- Analyze the sequence \[ a_n = 5^n 9^{-n} = \left(\frac{5}{9}\right)^n \].
- Determine whether this sequence approaches a finite limit as \( n \) approaches infinity or if it diverges.
- If the sequence converges, calculate and enter the limit in the provided box.
- If the sequence diverges, write "DIVERGES" in the box.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4acda8c7-3ed9-4816-93cd-e9a52e0b4613%2F5aa2bbe3-242b-4005-8b41-2a162947dc7f%2Fs83ss9t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Sequence Convergence or Divergence**
Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, enter DIVERGES.)
\[ a_n = 5^n 9^{-n} \]
\[ \lim_{n \rightarrow \infty} a_n = \boxed{} \]
**Instructions:**
- Analyze the sequence \[ a_n = 5^n 9^{-n} = \left(\frac{5}{9}\right)^n \].
- Determine whether this sequence approaches a finite limit as \( n \) approaches infinity or if it diverges.
- If the sequence converges, calculate and enter the limit in the provided box.
- If the sequence diverges, write "DIVERGES" in the box.
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