I am looking for some advice about approaching the following computations:
$$\lim\limits_{n\to\infty}{\prod\limits_{k=1}^{n}{\Bigr(1-\frac{2}{(k+1)\cdot(k+2)}\Bigr)}}=\large{?}$$ $$\lim\limits_{n\to\infty}{\prod\limits_{k=1}^{n}{\Bigr(1+\frac{2}{(k+1)\cdot(k+2)}\Bigr)}}=\large{?}$$
I tried to look for the logarithm of the limit and Taylor series, but nothing good came of it.
Thank you in advance.