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Let's take the example of finding the factorial of a number (of a positive integer). The factorial of N is N * (N-1) * (N-2) * (N-3) ... * 3 * 2 *1 It is the product of all integers between that number (including that number) and 1. For example, factorial 2 = 2*1 = 2 factorial 3 = 3*2*1 = 6 factorial 4 = 4*3*2*1= 24 Now you define a recursive function Fac (N) as Fac (N) = Fac (N-1) * N, with Fac(1) predefined as 1. Thus, Fac(N-1) = Fac(N-2) * (N-1) and Fac(N-2) = Fac(N-3) * (N-2) and thus recursion takes over until such time fac(1) needs to be evaluated. We know the value of Fac(1) which is set as 1. Thus we can evaluate Factorial(N) using recursion.
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Are all patterns recursive?
No, patterns with terms that are not based upon previous terms are not recursive. Example: i * i where i is the nth term of the pattern.
Will the explicit formula find the same answer when using the recursive formula?
It is often possible to find an explicit formula that gives the same answer as a given recursive formula - and vice versa. I don't think you can always find an explicit formula that gives the same answer.
What is the definition of recursive?
The term recursive refers to the recurrence or repetition.
What is recursive rule?
A recursive rule is one which can be applied over and over again to its own output
What is analysis of recursive program?
1) Recursive algorithms 2) Basic Principle 3) Analysis
