Check for convergence / divergence. Find the limit if convergence. 3n²-5n+1 2n +7 0 {a}= (a.} = {√²7m² +n+3) b) {b}= 2n-3, {c₁}={√10n} d) {d„ } = {In n − In(n + 1)} ) 3n-1
Check for convergence / divergence. Find the limit if convergence. 3n²-5n+1 2n +7 0 {a}= (a.} = {√²7m² +n+3) b) {b}= 2n-3, {c₁}={√10n} d) {d„ } = {In n − In(n + 1)} ) 3n-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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Test for convergence / divergence. Find the limit if result is convergence.
![### Problem 1: Check for Convergence / Divergence. Find the Limit if Convergence.
Consider the following sequences and determine whether they converge or diverge. If a sequence converges, find its limit.
#### a) Sequence \( \{a_n\} \)
\[ \{a_n\} = \left\{ \sqrt{\frac{3n^2 - 5n + 1}{7n^2 + n + 3}} \right\} \]
#### b) Sequence \( \{b_n\} \)
\[ \{b_n\} = \left\{ \left( \frac{2n + 7}{2n - 3} \right)^{3n - 1} \right\} \]
#### c) Sequence \( \{c_n\} \)
\[ \{c_n\} = \left\{ \sqrt[4]{10n} \right\} \]
#### d) Sequence \( \{d_n\} \)
\[ \{d_n\} = \{\ln n - \ln(n + 1)\} \]
For each sequence, analyze the terms \(a_n\), \(b_n\), \(c_n\), and \(d_n\) as \(n\) approaches infinity to determine whether the sequences converge or diverge. If a sequence converges, calculate its limit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc787ae5f-ecbe-4215-b4d0-f569392eb050%2F88da7898-65c5-4325-9062-0e4b7fa2b59b%2Fz7i5e4p_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 1: Check for Convergence / Divergence. Find the Limit if Convergence.
Consider the following sequences and determine whether they converge or diverge. If a sequence converges, find its limit.
#### a) Sequence \( \{a_n\} \)
\[ \{a_n\} = \left\{ \sqrt{\frac{3n^2 - 5n + 1}{7n^2 + n + 3}} \right\} \]
#### b) Sequence \( \{b_n\} \)
\[ \{b_n\} = \left\{ \left( \frac{2n + 7}{2n - 3} \right)^{3n - 1} \right\} \]
#### c) Sequence \( \{c_n\} \)
\[ \{c_n\} = \left\{ \sqrt[4]{10n} \right\} \]
#### d) Sequence \( \{d_n\} \)
\[ \{d_n\} = \{\ln n - \ln(n + 1)\} \]
For each sequence, analyze the terms \(a_n\), \(b_n\), \(c_n\), and \(d_n\) as \(n\) approaches infinity to determine whether the sequences converge or diverge. If a sequence converges, calculate its limit.
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