Convert recursive formula to explicit

Question

I have this:

f(1) = 1
f(n) = f(n-1)*(n/(n+2))

I have to convert it to it's explicit form, but I have absolutely no idea

Edit: the first elements are

1       0.3333333333333333 
2       0.16666666666666666 
3       0.1
4       0.06666666666666667
5       0.047619047619047616
6       0.03571428571428571
7       0.027777777777777776 
8       0.02222222222222222 
9       0.01818181818181818

Answer 1

$f(2)=f(1)\cdot \frac{2}{4}=\frac{2}{4}=\frac{1}{2}$

$f(3)=f(2)\cdot \frac{3}{5}=\frac{2}{4}\cdot \frac{3}{5}=\frac{3}{10}$

$f(4)=f(3)\cdot \frac{4}{6}=\frac{2}{4}\cdot \frac{3}{5}\cdot \frac{4}{6}$

$f(n)=\frac{\prod_{k=2}^{n}k}{\prod_{k=4}^{n+2}k}=\frac{6}{(n+1)(n+2)}$.