Find the First Term a_n=((n+4)!)/((n+5)!)

$a_{n} = \frac{(n + 4)!}{(n + 5)!}$

Step 1

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

$a_{1} = \frac{((1) + 4)!}{((1) + 5)!}$

Step 2

Simplify the factorials.

Add $1$ and $4$ .

$a_{1} = \frac{(5)!}{((1) + 5)!}$

Add $1$ and $5$ .

$a_{1} = \frac{(5)!}{(6)!}$

Step 3

Rewrite $(6)!$ as $6 \cdot 5!$ .

$a_{1} = \frac{(5)!}{6 \cdot 5!}$

Step 4

Cancel the common factor of $(5)!$ .

Cancel the common factor.

$a_{1} = \frac{(5)!}{6 \cdot 5!}$

Rewrite the expression.

$a_{1} = \frac{1}{6}$