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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**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 \( \ln a_n \to \ln L \).
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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