### Transcription for Educational Website---**Problem Statement**1. Find \(\lim_{n \to \infty} \sup(s_n)\) and \(\lim_{n \to \infty} \inf(s_n)\) for the sequence: \[ s_n = 1 + \frac{1}{n} \]2. Find \(\lim_{n \to \infty} \sup(s_n)\) and \(\lim_{n \to \infty} \inf(s_n)\) for the sequence: \[ s_n = n \]3. Find \(\lim_{n \to \infty} \sup(s_n)\) and \(\lim_{n \to \infty} \inf(s_n)\) for the sequence: \[ \{s_n\} = \{1, 0, 1, 0, 1, 0, \ldots\} \]**Explanation**- **1st Sequence:** \( s_n = 1 + \frac{1}{n} \) - As \( n \) approaches infinity, \( \frac{1}{n} \) approaches 0. So, \( s_n \) approaches 1. - **2nd Sequence:** \( s_n = n \) - As \( n \) approaches infinity, the sequence itself diverges to infinity. Therefore, the supremum also approaches infinity. - **3rd Sequence:** Alternating Sequence \( \{1, 0, 1, 0, 1, 0, \ldots\} \) - The sequence alternates between 1 and 0 indefinitely.**Conclusion**- For each sequence, identify the limiting behavior using the supremum and infimum concepts as required.---This transcription assists in understanding how to evaluate the limit superior and limit inferior for different types of sequences.

Name: ### Transcription for Educational Website---**Problem Statement**1. F
Uploaded: 2024-03-20T06:38:58.000Z
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Description: ### Transcription for Educational Website---**Problem Statement**1. Find \(\lim_{n \to \infty} \sup(s_n)\) and \(\lim_{n \to \infty} \inf(s_n)\) for the sequence: \[ s_n = 1 + \frac{1}{n} \]2. Find \(\lim_{n \to \infty} \sup(s_n)\) and \(\lim_