Write a recursive function for the following to calculate th

Write a recursive function for the following: to calculate the n^th Harmonic number. H_1 = 1 H_n = H_n-1 + 1/n To evaluate a polynomial of degree n (use a vector) at a value m using Horner\'s method.

Solution

// C++ nth harmonic number and polynomial evaluation using recursion

#include <iostream>
#include <vector>

using namespace std;

double ntharmonic(int n)
{
if(n == 1)
return 1.0;
else
return (1.0 / n) + ntharmonic(n - 1);
}

double evalPolynomial(vector<int> poly, int x, int n)
{
if (n < 0)
return 0;

double result = poly[n-1];
n--;

result = result + evalPolynomial(poly,x,n)*x;
return result;
}

int main()
{
int n;
cout << \"Enter positive intege N: \";
cin >>n;
cout << n << \" harmonic number: \" << ntharmonic(n) << endl;

std::vector<int> v;
v.push_back(1);
v.push_back(1);
v.push_back(1);
cout << \"Polynomial value: \" << evalPolynomial(v,2,v.size()) << endl;

return 0;
}

/*
output:

Enter positive intege N: 5
5 harmonic number: 2.28333

Polynomial value: 7

*/