Give a Recursive Definition of the Sequence a_n = n * a_{n-1} for n ≥ 1

To define the sequence a_n recursively, we need to establish a base case and a recursive case. The given sequence is defined as follows:

• Base Case: When n = 1, we set a_1 = 1.
• Recursive Case: For n > 1, we define a_n in terms of a_{n-1} with the formula: a_n = n * a_{n-1}.

This means that each term in the sequence is calculated by multiplying the current index n by the previous term in the sequence. This definition allows us to build the entire sequence step-by-step starting from the base case.

Thus, we have:

a(n) = 
  { 1,                  if n = 1,
  { n * a(n-1),       if n > 1.