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 H_n.
The harmonic series is as follows: 

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

// 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 formula
    // 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;
}

Java

// 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 formula
    // 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

Python 3

# 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 formula
    # 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

C#

// 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 formula
    // 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

PHP

<?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 formula
    // 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
?>

Javascript

<script>


// Javascript program to find
// N-th Harmonic Number

// Function to find N-th
// Harmonic Number
function nthHarmonic(N)
{
    // H1 = 1
    let harmonic = 1.00;

    // loop to apply the formula
    // Hn = H1 + H2 + H3 ... +
    // Hn-1 + Hn-1 + 1/n
    for (let i = 2; i <= N; i++)
    {
        harmonic += parseFloat(1) / i;
    }

    return harmonic;
}

// Driver Code

let N = 8;
document.write( nthHarmonic(N).toFixed(5));

// This code is contributed by bobby

</script>

Output:

2.71786

Time Complexity: O(N)

Auxiliary Space: O(1) as using constant space, since no extra space has been taken.