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:

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.

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?

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.