. Consider the following recursive algorithm for computing the sum of the first  n cubes. s(n)=13+23+33+…n3 Algorithm s(n) if(==1) return 1 else return (s(n-1)+n*n*n) End algorithm  Set up and solve recurrence relation for the number of times the basic   operation of the algorithm is executed

Consider the following recursive algorithm Algorithm Q(n)// Input: a positive integer nif n == 1 return 1else return Q(n-1)+2*n-1 1) Set up a recurrence relation for this function’s value and solve it to determine what this algorithm computes. 2) Setup a recurrence relation for the number of multiplication made by this algorithm and solve it to find the total number of multiplications that are executed.

Express the linear search algorithm as a recursive procedure

The n-th harmonic is the sum of the reciprocals of the first n natural numbers given by: 17 1.1 1 1 H₁ =Σ =1+=+=+ - 2 3 4 k=1 k +. + n (i) Write a recursive algorithm of this function returning, H, with nε N. (ii) Give a recurrence relation for the number of divisions the recursive algorithm calculates for an input n & N. iii) Solve the recurrence relation and give the O(n) of the algorithm.