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. |
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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; } |
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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. |
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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 |
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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. |
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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 ?> |
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Output:
2.283333
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