TheMathWorld

Question-80 Give a recursive  algorithm for finding the maximum of a finite set of integers , making use of the fact that the maximum of n integers is the larger…

Question-79 Give a recursive algorithm for finding the sum of the first n positive integers.   Solution procedure sum of first (n : positive integer) if  n = 1 then…

Question-78 A Recursive Algorithm for Computing n! Procedure factorial (n : nonnegative integer) if  n = 0 then return 1 else return n ·factorial (n – 1 ) { output…

Question-77 Give a recursive definition of the set of positive integers that are multiples of 5.   Solution 5   S , and 5x    S  if  x   S  .

Question-76 Let fn be the nth Fibonacci number. Prove that when n is a positive integer.   Solution The basis step (n = 1) is clear, since = 1 . Assume the…

Question-75 Give a recursive definition of the sequence {an} , n = 1, 2, 3, …… if  a)     an = 4n – 2.  b)    an = 3 + 3.(-1)n. c)    …

Question-74 Determine whether each of these proposed definitions is a valid recursive definitions of a function f from the set of nonnegative to the set of integers. If f is…

Question-73 Find f (2),  f(3), f(4), and  f(5) if f is defined recursively by f(0) = -1,  f(1) = 2, and for n = 1, 2, … a)     f (n…

Question-72 Prove that if A1 , A2 , …. , An and B1 , B2 … Bn are sets such that Aj Bj for j = 1, 2 ,…, n,…

Question-71 Use mathematical induction to prove that 3 divides + 2 n whenever n is a positive integer.   solution   The statement is true for the base case, n…