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The document you uploaded contains exercises on sequences ("ciągi") and limits of sequences ("granice ciągów"). Below are the key tasks from the first two sections of the document:

1. **Monotonicity of sequences**: Investigate whether the following sequences are increasing or decreasing:
   - \( a_n = \frac{1}{3n} \)
   - \( b_n = 2n - 2 \)
   - \( c_n = \frac{n^2}{n+2} \)

2. **Limits of sequences**: Calculate the limits of the following sequences (if they exist):
   - \( \lim_{n \to \infty} \frac{17n + 35}{3n + 1} \)
   - \( \lim_{n \to \infty} \frac{3n^3 + 23n^2 + 52n + 45}{n^3 + 2n^2 + 1} \)
   - \( \lim_{n \to \infty} \frac{2n^2 + 5n + 1}{n^2 + 25} \)
   - And several other limit expressions.

Would you like me to solve any specific problem from this document or provide a detailed solution for a sequence? Feel free to choose a task.

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**Related Questions:**
1. How do you determine whether a sequence is increasing or decreasing?
2. What is the general method to find the limit of a sequence as \( n \to \infty \)?
3. How do you apply L'Hôpital's Rule to solve indeterminate forms?
4. What role does the degree of polynomials play in finding limits of rational functions?
5. Can you explain the difference between bounded and unbounded sequences?

**Tip**: For limits involving rational functions, comparing the degrees of the numerator and denominator is key to determining the behavior as \( n \to \infty \).

The document contains exercises related to sequences and limits of sequences. Examples include: determining the monotonicity of sequences and calculating the limits of various sequences such as \( \lim_{n \to \infty} \frac{17n + 35}{3n + 1} \) and \( \lim_{n \to \infty} \frac{2n^2 + 5n + 1}{n^2 + 25} \).

Explore problems on the monotonicity and limits of sequences, such as determining whether sequences are increasing or decreasing and finding the limits of complex rational functions. Learn how to apply key mathematical techniques such as L'Hôpital's Rule and polynomial degree comparison.

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