If `a_(1)=1,a_(n+1)=(1)/(n+1)a_(n),a ge1`, then prove by induction that `a_(n+1)=(1)/((n+1)!)n in N`.

Explanation

To prove that \( a_{n+1} = \frac{1}{(n+1)!} \) for \( n \in \mathbb{N} \) using mathematical induction, we will follow these steps:

### Step 1: Base Case
We start with the base case where \( n = 1 \).

Given:
\[
a_1 = 1
...