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++ 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 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 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. |
# 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# 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 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 ?> |
<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.