X1=2024 dan xn=n/2xn-1 untuk bilangan n>1 hasil dari 2024πi=1×i

To solve this problem, let's start by understanding the recursive formula provided and the expression \( 2024 \prod_{i=1}^n i \).

### Understanding the Recursive Formula
Given:
- \( x_1 = 2024 \)
- \( x_n = \frac{n}{2} x_{n-1} \) for \( n > 1 \)

This recursive relation shows that each term \( x_n \) is calculated based on the previous term \( x_{n-1} \), multiplied by \( \frac{n}{2} \).

### Calculating the General Expression for \( x_n \)
Let's compute the first few values to identify a pattern:

\[
\begin{align*}
x_1 &= 2024, \\
x_2 &= \frac{2}{2} x_1 = 1 \times 2024 = 2024, \\
x_3 &= \frac{3}{2} x_2 = \frac{3}{2} \times 2024 = 3036, \\
x_4 &= \frac{4}{2} x_3 = 2 \times 3036 = 6072, \\
x_5 &= \frac{5}{2} x_4 = \frac{5}{2} \times 6072 = 15180.
\end{align*}
\]

We see that the formula indeed builds upon the previous term multiplied by \( \frac{n}{2} \).

### Expression \( 2024 \prod_{i=1}^n i \)
The expression \( 2024 \prod_{i=1}^n i \) involves multiplying 2024 by the product of all integers from 1 to \( n \). This can be written as:

\[
2024 \times (1 \times 2 \times 3 \times \ldots \times n) = 2024 \times n!.
\]

This shows that the expression is 2024 multiplied by the factorial of \( n \).

### Conclusion
The result for \( x_n \) in terms of the recursive formula involves repeatedly applying the multiplication by \( \frac{n}{2} \), and the expression \( 2024 \prod_{i=1}^n i \) is equal to \( 2024 \times n! \).

### Follow-up Questions:
1. Do you want to find the value of \( x_n \) for a specific \( n \)?
2. Are you interested in the derivation of a closed formula for \( x_n \)?
3. Would you like to explore how factorial growth impacts the values of \( x_n \)?
4. Do you want to understand the convergence properties of this sequence?
5. Would you like to see the computation of \( x_n \) for higher values of \( n \)?

#### Tip:
When dealing with recursive sequences, try calculating the first few terms to identify patterns that can help generalize the formula!

Explore the recursive sequence x_n = (n / 2) * x_{n-1} starting from x_1 = 2024 and the product expression involving factorials 2024 * n!. Learn how to calculate terms in the sequence and understand the relation to factorial growth. Suitable for high school students in Grades 10-12.

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