Prove that $(k + 1)^{2} . k! = (k + 1) (k + 1)!$

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Solution

we know that,
$1.2.3.4................ (n - 2) (n - 1) n = n!$
i.e., $(n - 1)! . n = n!$

Now $(k + 1)^{2} . k! = (k + 1) (k + 1) . k! = (k + 1) . (k + 1)!$

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