<s>[INST] A finite product : $\prod_{k=0}^{n-1}(1-\frac{1}{n-1+k})$ Find the maximum and minimum of the following products : 
$A)$ $\prod_{k=0}^{n-1}(1-\frac{1}{n-1+k})$
$B)$ $\prod_{k=0}^{n-1}(1-\frac{1}{n+1-k})$
My idea is : 
$n-1+k>k$ then : $\frac{1}{n-1+k}<\frac{1}{k}$ 
We obtain : 
$\prod_{k=0}^{n-1}(1-\frac{1}{k})$ 
But I don't have ideas to complete my work , and is my attempt correct ?
 [/INST] HINT: (Assuming $ n \geq 2 $)
$\prod_{k=0}^{n-1}(1-\frac{1}{n+k-1}) = \prod_{k=0}^{n-1}\frac{n+k-2}{n+k-1} = \frac{n-2}{n+(n-1)-1} = \frac{1}{2} \cdot \frac{n-2}{n-1}$
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