Find the Second Term a_n=n*(n+1)!

$a_{n} = n \cdot (n + 1)!$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$a_{2} = (2) \cdot ((2) + 1)!$

Step 2

Add $2$ and $1$ .

$a_{2} = 2 \cdot (3)!$

Step 3

Expand $(3)!$ to $3 \cdot 2 \cdot 1$ .

$a_{2} = 2 \cdot (3 \cdot 2 \cdot 1)$

Step 4

Multiply $3 \cdot 2 \cdot 1$ .

Multiply $3$ by $2$ .

$a_{2} = 2 \cdot (6 \cdot 1)$

Multiply $6$ by $1$ .

$a_{2} = 2 \cdot 6$

Step 5

Multiply $2$ by $6$ .

$a_{2} = 12$