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The image contains a set of mathematical statements in Russian, asking to select the correct ones. The statements involve sequences, limits, and bounds.

Here is a translation of the text:

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**Select the correct statements.**

1. Consider the set of partial limits of the sequence \( \{a_n\} \). Let the number \( M \) satisfy the condition: \( M \) is a partial limit of the sequence \( \{a_n\} \). For any other convergent subsequence \( \{a_{n_k}\} \), \( \lim_{k \to \infty} a_{n_k} \geq M \). Then the number \( M \) is called the infimum of the sequence \( \{a_n\} \).

2. Let the sequences \( \{a_n\} \) and \( \{\gamma_n\} \) be infinitesimally small, and \( \{b_n\} \), where \( b_n = \alpha_n \cdot a_n + \beta_n \cdot \gamma_n \), is also infinitesimally small.

3. Consider the sequences \( \{a_n\} \), \( \{b_n\} \), and \( \{c_n\} \). Let the sequences \( \{a_n\} \), \( \{b_n\} \) converge, \( \lim_{n \to \infty} a_n = a \), \( \lim_{n \to \infty} b_n = a \), and the general terms of the sequences satisfy the inequalities \( a_n \leq c_n \leq b_n \). Then the sequence \( \{c_n\} \) also converges, and \( \lim_{n \to \infty} c_n = a \).

4. Let the sequences \( \{a_n\} \), \( \{\gamma_n\} \) be infinitesimally small, and \( \{b_n\} \), where \( b_n = \alpha_n \cdot a_n + \frac{1}{\beta_n} \), is also infinitesimally small.

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These statements seem to focus on convergence, limits, and small sequences. Let me know which part you'd like to explore further, and I can provide detailed insights into the correct ones.

Would you like help solving or explaining any specific statement?

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Here are 5 related questions to extend your understanding:

1. What is a partial limit of a sequence, and how is it related to convergence?
2. How do inequalities like \( a_n \leq c_n \leq b_n \) help in proving the convergence of sequences?
3. What are infinitesimally small sequences, and how are they treated in analysis?
4. How does the concept of a limit relate to subsequences and their behavior?
5. What is the significance of the infimum in the context of sequences?

**Tip:** When studying convergence of sequences, always verify whether the sequence is bounded and whether its subsequences have limits—these are key properties to determine convergence.

Select the correct statements involving sequences, limits, and bounds from the provided options in Russian.

This problem explores the convergence of sequences and their bounds, focusing on partial limits, the infimum, and infinitesimally small sequences. Ideal for university-level mathematics students.

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