Question

example 8: solve for n.
a) \\(\frac{(n + 3)!}{(n + 2)!} = 10\\)

Explanation:

Step1: Simplify factorial fraction

Recall that $(n+3)! = (n+3) \times (n+2)!$, so:
$\frac{(n+3)!}{(n+2)!} = n+3$

Step2: Set up simplified equation

Substitute into original equation:
$n+3 = 10$

Step3: Solve for n

Subtract 3 from both sides:
$n = 10 - 3$

Answer:

$n=7$