Program to find sum of series 1 + 1/2 + 1/3 + 1/4 + .. + 1/n

If inverse of a sequence follows rule of an A.P i.e, Arithmetic progression, then it is said to be in Harmonic 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 the common difference.
We can use a for loop to find sum. 

C++

// C++ program to find sum of series
#include <iostream>
using namespace std;

// Function to return sum of
// 1/1 + 1/2 + 1/3 + ..+ 1/n
class gfg
{

public : double sum(int n)
{
    double i, s = 0.0;
    for (i = 1; i <= n; i++)
    s = s + 1/i;
    return s;
}
};

// Driver code
int main()
{
    gfg g;
    int n = 5;
    cout << "Sum is " << g.sum(n);
    return 0;
}

// This code is contributed by SoM15242.

C

// C program to find sum of series
#include <stdio.h>

// Function to return sum of 1/1 + 1/2 + 1/3 + ..+ 1/n
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;
}

Java

// Java Program to find sum of series
import java.io.*;

class GFG {

    // Function to return sum of
    // 1/1 + 1/2 + 1/3 + ..+ 1/n
    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));

    }
}

// This code is contributed by Nikita Tiwari.

Python3

# Python program to find the sum of 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))

# This code is contributed by Chinmoy Lenka

C#

// C# Program to find sum of series
using System;

class GFG {

    // Function to return sum of
    // 1/1 + 1/2 + 1/3 + ..+ 1/n
    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));

    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP program to find sum of series

// Function to return sum of
// 1/1 + 1/2 + 1/3 + ..+ 1/n
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));

//This code is contributed by vt_m
?>

Javascript

<script>
// javascript Program to find sum of series

// Function to return sum of
// 1/1 + 1/2 + 1/3 + ..+ 1/n
function sum(n)
{
  var i, s = 0.0;
  for (i = 1; i <= n; i++)
      s = s + 1/i;
  return s;
}

// Driven Program
var n = 5;
document.write(sum(n).toFixed(5));

// This code is contributed by Amit Katiyar
</script>

Output:

2.283333

Time Complexity: O(n)

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