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29 November, 11:39

Provide a recursive definition of the function f (n) = (n+1) !.

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  1. 29 November, 12:09
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    See definition below

    Step-by-step explanation:

    Since we have to give a recursive definition, we must give a initial value f (0). Additionally, the value of f (n) must depend on the value of f (n-1) for all n≥1.

    The required value of f (0) is (0+1) !=1!=1.

    Now, the factorial itself is a recursive function, because (n+1) ! = (n+1) n!. In terms of f, this means that f (n) = (n+1) f (n-1) for all n≥1.

    Then, our definition is: f:N→N is defined by

    f (0) = 1. For n≥1, f (n) = (n+1) f (n-1).
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