Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 1 1 1 1 1 1 { 2 7' 5' lim an = n-00
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 1 1 1 1 1 1 { 2 7' 5' lim an = n-00
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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![## Sequence Convergence or Divergence
### Problem Statement
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
### Sequence
\[ \left\{ \frac{1}{4}, \frac{1}{2}, \frac{1}{5}, \frac{1}{3}, \frac{1}{6}, \frac{1}{4}, \frac{1}{7}, \frac{1}{5}, \ldots \right\} \]
### Limit Calculation
\[ \lim_{{n \to \infty}} a_n = \boxed{\ \ \ } \]
In the text above, the sequence is represented as a set of fractions, each separated by a comma and enclosed in curly braces. The limit of the sequence is to be calculated symbolically as \( n \) approaches infinity, and the result should be filled in the provided box. If the sequence does not converge, indicate it by writing "DNE" (Does Not Exist).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1148f2e-12e2-4d7a-aa19-e54736499ad8%2Fc3da289c-d09d-477f-a050-6ace4d2c4cd0%2Fuf909kw_processed.png&w=3840&q=75)
Transcribed Image Text:## Sequence Convergence or Divergence
### Problem Statement
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
### Sequence
\[ \left\{ \frac{1}{4}, \frac{1}{2}, \frac{1}{5}, \frac{1}{3}, \frac{1}{6}, \frac{1}{4}, \frac{1}{7}, \frac{1}{5}, \ldots \right\} \]
### Limit Calculation
\[ \lim_{{n \to \infty}} a_n = \boxed{\ \ \ } \]
In the text above, the sequence is represented as a set of fractions, each separated by a comma and enclosed in curly braces. The limit of the sequence is to be calculated symbolically as \( n \) approaches infinity, and the result should be filled in the provided box. If the sequence does not converge, indicate it by writing "DNE" (Does Not Exist).
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