Program to find sum of harmonic series

Harmonic series is inverse of a arithmetic progression. In general, the terms in a harmonic progression can be denoted as 1/a, 1/(a + d), 1/(a + 2d), 1/(a + 3d) …. 1/(a + nd).
As Nth term of AP is given as ( a + (n – 1)d). Hence, Nth term of harmonic progression is reciprocal of Nth term of AP, which is 1/(a + (n – 1)d), where “a” is the 1st term of AP and “d” is a common difference.

Method #1: Simple approach

C

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// C program to find sum of harmonic series
#include <stdio.h>
  
// Function to return sum of harmonic series
double sum(int n)
{
  double i, s = 0.0;
  for (i = 1; i <= n; i++)
      s = s + 1/i;
  return s;
}
  
int main()
{
    int n = 5;
    printf("Sum is %f", sum(n));
    return 0;
}

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Java

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// Java Program to find sum of harmonic series
import java.io.*;
  
class GFG {
      
    // Function to return sum of
    // harmonic series
    static double sum(int n)
    {
      double i, s = 0.0;
      for (i = 1; i <= n; i++)
          s = s + 1/i;
      return s;
    }
   
     
    // Driven Program
    public static void main(String args[])
    {
        int n = 5;
        System.out.printf("Sum is %f", sum(n));        
    }
}

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Python3

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# Python program to find the sum of harmonic series
  
def sum(n):
    i = 1
    s = 0.0
    for i in range(1, n+1):
        s = s + 1/i;
    return s;
  
# Driver Code 
n = 5
print("Sum is", round(sum(n), 6))

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C#

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// C# Program to find sum of harmonic series
using System;
  
class GFG {
      
    // Function to return sum of
    // harmonic series
    static float sum(int n)
    {
        double i, s = 0.0;
          
        for (i = 1; i <= n; i++)
            s = s + 1/i;
              
        return (float)s;
    }
  
      
    // Driven Program
    public static void Main()
    {
        int n = 5;        
        Console.WriteLine("Sum is "
                           + sum(n));        
    }
}

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PHP

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<?php
// PHP program to find sum of harmonic series
  
// Function to return sum of
// harmonic series
function sum( $n)
{
    $i;
    $s = 0.0;
    for ($i = 1; $i <= $n; $i++)
        $s = $s + 1 / $i;
    return $s;
}
  
    // Driver Code
    $n = 5;
    echo("Sum is ");
    echo(sum($n));
      
?>

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Output:

Sum is 2.283333

Method #2: Using recursion

Java

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// Java program to find sum of 
// harmonic series using recursion 
import java.io.*; 
  
class GFG 
  
float sum(float n) 
    // Base condition 
    if (n < 2
        return 1
  
    else
        return 1 / n + (sum(n - 1)); 
  
// Driven Code 
public static void main(String args[]) 
  GFG g = new GFG(); 
  System.out.println(g.sum(8)); 
  System.out.print(g.sum(10)); 
  
// This code is contributed by Shivi_Aggarwal 

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Python 3

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# Python program to find sum of
# harmonic series using recursion
  
def sum(n):
  
    # Base condition
    if n < 2:
        return 1
  
    else:
        return 1 / n + (sum(n - 1))
          
print(sum(8))
print(sum(10))

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PHP

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<?php
// PHP program to find sum of 
// harmonic series using recursion 
  
function sum($n)
{
  
    // Base condition 
    if ($n < 2)
        return 1;
  
    else
        return 1 / $n + (sum($n - 1)); 
  
// Driver Code
echo sum(8) . "\n";
echo sum(10);
  
// This code is contributed by Ryuga
?>

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Output:

2.7178571428571425
2.9289682539682538


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Improved By : Ryuga, Shivi_Aggarwal