For doing the lab activity: 1) Apply Recursive function technique to solve Problem 1 and 2. (Do not use iterative method) 2) Use map, filter, reduce and lambda functions to solve the problem 3. 1.Evaluate Binomial Coefficient. nCr=n! / (r! *(n-r)!) 2. Fibonacci Numbers (Sequence): 0, 1, 1, 2, 3, 5, 8 .
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- 8- Determine if each of the following recursive definition is a valid recursive definition of a function f from a set of non-negative integers. If f is well defined, find a formula for f(n) where n is non- negative and prove that your formula is valid. a. f(0) = 2,f(1) = 3, f(n) = f(n-1)-1 for n ≥ 2 b. f(0) = 1,f(1) = 2, f(n) = 2f (n-2) for n = 2a)Write a recursive definition for the set of odd positive integers. b)Use master theorem to find the solution to the recurrence relation f(n) = 4f(n/2) + 2? ! ,when n = 2" , where k is a positive integer and f(1) = 1.2- Draw the recursion trace for the execution of function reverse (S, 0, 5) on S = [4, 3, 6, 2, 6]. (Lecture recursion III)
- Find a recursive definition for the sequence 5, 7, 10, 14, 19,... for n>1. How do I find the equation/recursive definition for this?Consider the following problems for recursive definition/solution. Answer the following questions. [Remember that a recursive definition/solution requires base case and recursive case] We learned that its power set has 2" elements when a set has n elements. Define it in a recursive solution.1. For the function defined recursively by f(0)=5 and f(n)=4f (n-1)+3, answer the following: a. Find a closed form representation for this function. Your closed form should not include any series. b. Prove that your representation is correct using a formal inductive argument.
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