4. Determine lim 1 2n), and prove it. n+1 n+ 2 Hint: use the Squeeze Theorem, modeling your work on Example 5.2C. You may assume: if an → L, with a, > 0 and L> 0, then In an → In L.
4. Determine lim 1 2n), and prove it. n+1 n+ 2 Hint: use the Squeeze Theorem, modeling your work on Example 5.2C. You may assume: if an → L, with a, > 0 and L> 0, then In an → In L.
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
![**Determine**
\[
\lim \left( \frac{1}{n+1} + \frac{1}{n+2} + \ldots + \frac{1}{2n} \right),
\]
and prove it.
**Hint:** Use the Squeeze Theorem, modeling your work on Example 5.2C. You may assume: if \( a_n \to L \), with \( a_n > 0 \) and \( L > 0 \), then \( \ln a_n \to \ln L \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bd9bd0-40fd-4172-a50a-abb52eb6a8c1%2Faf37696e-46fa-4c3b-a1f0-68f914e5c5dc%2F2vkt5tg_processed.png&w=3840&q=75)
Transcribed Image Text:**Determine**
\[
\lim \left( \frac{1}{n+1} + \frac{1}{n+2} + \ldots + \frac{1}{2n} \right),
\]
and prove it.
**Hint:** Use the Squeeze Theorem, modeling your work on Example 5.2C. You may assume: if \( a_n \to L \), with \( a_n > 0 \) and \( L > 0 \), then \( \ln a_n \to \ln L \).
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