# Convert recursive formula to explicit

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

• Did you compute $f(2)$, $f(3)$ and $f(4)$? Commented Sep 6, 2022 at 22:20
• I did, they are 1/3,1/6,1/10,1/15 Commented Sep 6, 2022 at 22:22
• I don't think so. Commented Sep 6, 2022 at 22:25
• So does $f(1) = 1$ or $f(1) = 0.3333333333333333$? Commented Sep 6, 2022 at 22:48
• @AnneBauval. Bonjour, voisine ! Commented Sep 7, 2022 at 12:31

$$f(2)=f(1)\cdot \frac{2}{4}=\frac{2}{4}=\frac{1}{2}$$
$$f(3)=f(2)\cdot \frac{3}{5}=\frac{2}{4}\cdot \frac{3}{5}=\frac{3}{10}$$
$$f(4)=f(3)\cdot \frac{4}{6}=\frac{2}{4}\cdot \frac{3}{5}\cdot \frac{4}{6}$$
$$f(n)=\frac{\prod_{k=2}^{n}k}{\prod_{k=4}^{n+2}k}=\frac{6}{(n+1)(n+2)}$$.