Given the value of n, we need to find the sum of the series where i-th term is sum of first i natural numbers.
Examples :
Input : n = 5 Output : 35 Explanation : (1) + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) = 35 Input : n = 10 Output : 220 Explanation : (1) + (1+2) + (1+2+3) + .... +(1+2+3+4+.....+10) = 220
Naive Approach :
Below is implementation of above series :
C++
// CPP program to find sum of given series #include <bits/stdc++.h> using namespace std;
// Function to find sum of given series int sumOfSeries( int n)
{ int sum = 0;
for ( int i = 1 ; i <= n ; i++)
for ( int j = 1 ; j <= i ; j++)
sum += j;
return sum;
} // Driver Function int main()
{ int n = 10;
cout << sumOfSeries(n);
return 0;
} |
Java
// JAVA Code For Sum of the series import java.util.*;
class GFG {
// Function to find sum of given series
static int sumOfSeries( int n)
{
int sum = 0 ;
for ( int i = 1 ; i <= n ; i++)
for ( int j = 1 ; j <= i ; j++)
sum += j;
return sum;
}
/* Driver program to test above function */
public static void main(String[] args)
{
int n = 10 ;
System.out.println(sumOfSeries(n));
}
} // This code is contributed by Arnav Kr. Mandal. |
Python
# Python3 program to find sum of given series # Function to find sum of series def sumOfSeries(n):
return sum ([i * (i + 1 ) / 2 for i in range ( 1 , n + 1 )])
# Driver Code if __name__ = = "__main__" :
n = 10
print (sumOfSeries(n))
|
C#
// C# Code For Sum of the series using System;
class GFG {
// Function to find sum of given series
static int sumOfSeries( int n)
{
int sum = 0;
for ( int i = 1; i <= n; i++)
for ( int j = 1; j <= i; j++)
sum += j;
return sum;
}
/* Driver program to test above function */
public static void Main()
{
int n = 10;
Console.Write(sumOfSeries(n));
}
} // This code is contributed by vt_m. |
PHP
<?php // PHP program to find // sum of given series // Function to find // sum of given series function sumOfSeries( $n )
{ $sum = 0;
for ( $i = 1 ; $i <= $n ; $i ++)
for ( $j = 1 ; $j <= $i ; $j ++)
$sum += $j ;
return $sum ;
} // Driver Code $n = 10;
echo (sumOfSeries( $n ));
// This code is contributed by Ajit. ?> |
Javascript
<script> // JavaScript Program for Sum of the series // Function to find sum of given series
function sumOfSeries(n)
{
let sum = 0;
for (let i = 1 ; i <= n ; i++)
for (let j = 1 ; j <= i ; j++)
sum += j;
return sum;
}
// Driver code let n = 10;
document.write(sumOfSeries(n));
</script> |
Output :
220
Efficient Approach :
Let
an = Σn1= = Sum of n-terms of series Σn1 an = Σn1 = Σ + Σ = * + * =
Below is implementation of above approach :
C++
// CPP program to find sum of given series #include <bits/stdc++.h> using namespace std;
// Function to find sum of given series int sumOfSeries( int n)
{ return (n * (n + 1) * (2 * n + 4)) / 12;
} // Driver Function int main()
{ int n = 10;
cout << sumOfSeries(n);
} |
Java
// JAVA Code For Sum of the series import java.util.*;
class GFG {
// Function to find sum of given series
static int sumOfSeries( int n)
{
return (n * (n + 1 ) *
( 2 * n + 4 )) / 12 ;
}
/* Driver program to test above function */
public static void main(String[] args)
{
int n = 10 ;
System.out.println(sumOfSeries(n));
}
} // This code is contributed by Arnav Kr. Mandal. |
Python
# Python program to find sum of given series # Function to find sum of given series def sumOfSeries(n):
return (n * (n + 1 ) * ( 2 * n + 4 )) / 12 ;
# Driver function if __name__ = = '__main__' :
n = 10
print (sumOfSeries(n))
|
C#
// C# Code For Sum of the series using System;
class GFG {
// Function to find sum of given series
static int sumOfSeries( int n)
{
return (n * (n + 1) * (2 * n + 4)) / 12;
}
/* Driver program to test above function */
public static void Main()
{
int n = 10;
Console.Write(sumOfSeries(n));
}
} // This code is contributed by vt_m. |
PHP
<?php // PHP program to find // sum of given series // Function to find // sum of given series function sumOfSeries( $n )
{ return ( $n * ( $n + 1) *
(2 * $n + 4)) / 12;
} // Driver Code $n = 10;
echo (sumOfSeries( $n ));
// This code is contributed by Ajit. ?> |
Javascript
<script> // JavaScript program For Sum of the series // Function to find sum of given series function sumOfSeries(n)
{
return (n * (n + 1) *
(2 * n + 4)) / 12;
}
// Driver code let n = 10;
document.write(sumOfSeries(n));
</script> |
Output :
220
Time Complexity: O(1)
Auxiliary Space: O(1)