Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + …… + (1+2+3+4+…+n)
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 term of the series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4)…(1 + 2 + 3 +..n) be denoted as an
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)
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