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 = 5print("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.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
