https://r2.erweima.ai/mathbot/image/1727118382510fi3tj15y.jpg

The image contains a mathematical sequence problem where the sequence is defined as \( u_n = \frac{3}{n^2} \). The question asks for the behavior or property of this sequence as \( n \) increases.

### Analyzing the Sequence:
The given sequence is:

\[
u_n = \frac{3}{n^2}
\]

As \( n \) increases (i.e., as \( n \to \infty \)), the term \( u_n \) gets smaller and approaches 0. To be more specific:

- \( u_n \) is **decreasing** as \( n \) increases. This is because as \( n \) increases, the denominator \( n^2 \) increases, causing the fraction to decrease.
- The sequence is **positive** for all \( n \), as both the numerator and the square of \( n \) are positive.
- \( u_n \to 0 \) as \( n \to \infty \), meaning the sequence converges to 0.

### Answer Options:
From the given choices, the correct property of this sequence \( u_n = \frac{3}{n^2} \) is that it is **"completely decreasing" (متناقصة تماماً)**.

So, the correct answer is:

\[
\boxed{B}
\]

Do you want further details or explanations on this? 

Here are 5 related questions:
1. What is the limit of \( u_n \) as \( n \to \infty \)?
2. How do we prove that \( u_n = \frac{3}{n^2} \) is decreasing for all \( n \)?
3. What does it mean for a sequence to be monotonic?
4. Can we determine if the sequence is bounded?
5. What is the difference between a decreasing sequence and a strictly decreasing sequence?

**Tip**: When analyzing sequences, always check whether they converge or diverge and if they are monotonic (increasing or decreasing).

عند دراسة اطّراد المتتالية: un = 3/n^2 نجد أنها؟

Explore the behavior of the sequence u_n = 3/n^2 as n increases. This problem analyzes the monotonicity and limit of the sequence, showing that it is completely decreasing as n approaches infinity. Suitable for Grades 10-12.

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