Question

$frac{(n-1)!}{n!`} - frac{n!}{(n+1)!}$

Answer 1

n!=1*2*3*....*(n-1)*n
n!/(n-1)!=n
(n-1)!/n!=1/n
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$frac{(n-1)!}{n!} - frac{n!}{(n+1)!} = frac{1}{n} - frac{1}{n+1} = frac{n+1-n}{n(n+1)} = frac{1}{n(n+1)}$