By trying small values of n, you can see that for n > 4 ,
(n+1) n-1 < n n < (n-1) n+1 .
One way to prove this is to consider the ratios
n n (n-1) n+1
and
(n+1) n-1 n n

and show that they are greater than 1 for n > 4 .

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