Program to find the Nth Harmonic Number

Given a number N. The task is to find the Nth Harmonic Number.

Let the nth harmonic number be Hn.

The harmonic series is as follows:




H1 = 1
H2 = H1 + 1/2
H3 = H2 + 1/3
H4 = H3 + 1/4
.
.
.
Hn = Hn-1 + 1/n

Examples:

Input : N = 5
Output : 2.45

Input : N = 9
Output : 2.71786

The idea is to traverse from H1 and then consecutively keep finding H2 from H1, H3 from H2 ….. and so on.

Below is the program to find N-th Harmonic Number:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to find N-th Harmonic Number
  
#include <iostream>
using namespace std;
  
// Function to find N-th Harmonic Number
double nthHarmonic(int N)
{
    // H1 = 1
    float harmonic = 1.00;
  
    // loop to apply the forumula 
    // Hn = H1 + H2 + H3 ... + Hn-1 + Hn-1 + 1/n
    for (int i = 2; i <= N; i++) {
        harmonic += (float)1 / i;
    }
  
    return harmonic;
}
  
// Driver Code
int main()
{
    int N = 8;
      
    cout<<nthHarmonic(N);
      
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find N-th Harmonic Number
  
import java.io.*;
  
class GFG {
      
// Function to find N-th Harmonic Number
static double nthHarmonic(int N)
{
    // H1 = 1
    float harmonic = 1;
  
    // loop to apply the forumula 
    // Hn = H1 + H2 + H3 ... + Hn-1 + Hn-1 + 1/n
    for (int i = 2; i <= N; i++) {
        harmonic += (float)1 / i;
    }
  
    return harmonic;
}
  
// Driver Code
  
    public static void main (String[] args) {
            int N = 8;
      
    System.out.print(nthHarmonic(N));
      
    }
}
// This code is contributed 
// by ajit

chevron_right


Python 3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to find 
# N-th Harmonic Number
  
# Function to find N-th Harmonic Number 
def nthHarmonic(N) :
  
    # H1 = 1 
    harmonic = 1.00
  
    # loop to apply the forumula 
    # Hn = H1 + H2 + H3 ... + 
    # Hn-1 + Hn-1 + 1/n 
    for i in range(2, N + 1) :
        harmonic += 1 / i
  
    return harmonic
      
# Driver code     
if __name__ == "__main__" :
  
    N = 8
    print(round(nthHarmonic(N),5))
  
# This code is contributed by ANKITRAI1

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find N-th Harmonic Number
using System;
  
class GFG 
{
      
// Function to find N-th Harmonic Number
static double nthHarmonic(int N)
{
    // H1 = 1
    float harmonic = 1;
  
    // loop to apply the forumula 
    // Hn = H1 + H2 + H3 ... + 
    // Hn-1 + Hn-1 + 1/n
    for (int i = 2; i <= N; i++)
    {
        harmonic += (float)1 / i;
    }
  
    return harmonic;
}
  
// Driver Code
static public void Main ()
{
    int N = 8;
      
    Console.Write(nthHarmonic(N));
}
}
  
// This code is contributed 
// by Raj

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find 
// N-th Harmonic Number
  
// Function to find N-th
// Harmonic Number
function nthHarmonic($N)
{
    // H1 = 1
    $harmonic = 1.00;
  
    // loop to apply the forumula 
    // Hn = H1 + H2 + H3 ... + 
    // Hn-1 + Hn-1 + 1/n
    for ($i = 2; $i <= $N; $i++) 
    {
        $harmonic += (float)1 / $i;
    }
  
    return $harmonic;
}
  
// Driver Code
$N = 8;
echo nthHarmonic($N);
      
// This code is contributed 
// by Shivi_Aggarwal
?>

chevron_right


Output:

2.71786

Time Complexity: O(N)



My Personal Notes arrow_drop_up

Maths is the language of nature

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Ryuga, Shivi_Aggarwal, jit_t, R_Raj