d(1)= 1, d(n)= n x d(n-1) for n>2 first five terms

The function \( d(n) \) is defined as:

- \( d(1) = 1 \)
- \( d(n) = n \times d(n-1) \) for \( n > 2 \)

This is a recursive function, similar to the factorial function. Let's calculate the first five terms:

1. \( d(1) = 1 \)
2. \( d(2) = 2 \times d(1) = 2 \times 1 = 2 \)
3. \( d(3) = 3 \times d(2) = 3 \times 2 = 6 \)
4. \( d(4) = 4 \times d(3) = 4 \times 6 = 24 \)
5. \( d(5) = 5 \times d(4) = 5 \times 24 = 120 \)

So, the first five terms are:
\[
d(1) = 1, \quad d(2) = 2, \quad d(3) = 6, \quad d(4) = 24, \quad d(5) = 120
\]

Would you like more details or explanations on this? Here are 5 related questions to explore further:

1. What is the general formula for factorial functions?
2. How does recursion work in mathematical sequences?
3. Can you calculate \( d(6) \) using the same pattern?
4. What are some practical uses of factorial functions?
5. How would you prove the recursion formula using induction?

**Tip:** Recursive functions rely on a base case to prevent infinite loops and allow for calculations to stop after finite steps.

d(1) = 1, d(n) = n x d(n-1) for n > 2 first five terms

Learn how to calculate the first five terms of a recursive function d(n) = n × d(n-1), similar to the factorial sequence. This problem introduces key concepts such as recursion and the factorial function. Suitable for students in Grades 9-12.

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