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kati45 [8]
3 years ago
8

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

Mathematics
1 answer:
fiasKO [112]3 years ago
8 0

Answer:

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

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