Sum of the series 1 + (1+2) + (1+2+3) + (1+2+3+4) + ...... + (1+2+3+4+...+n)

09 Sep, 2021
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++
Java
Python
C#
PHP
Javascript
// CPP program to find sum of given series#include <bits/stdc++.h>using namespace std; // Function to find sum of given seriesint 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 Functionint main(){    int n = 10;    cout << sumOfSeries(n);    return 0;}
// JAVA Code For Sum of the seriesimport 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.
# Python3 program to find sum of given series # Function to find sum of seriesdef sumOfSeries(n):    return sum([i*(i+1)/2 for i in range(1, n + 1)]) # Driver Codeif __name__ == "__main__":    n = 10    print(sumOfSeries(n))
// C# Code For Sum of the seriesusing 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 program to find// sum of given series // Function to find// sum of given seriesfunction 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.?>
<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++
Java
Python
C#
PHP
Javascript
// CPP program to find sum of given series#include <bits/stdc++.h>using namespace std; // Function to find sum of given seriesint sumOfSeries(int n){    return (n * (n + 1) * (2 * n + 4)) / 12;} // Driver Functionint main(){    int n = 10;    cout << sumOfSeries(n);}
// JAVA Code For Sum of the seriesimport 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 program to find sum of given series # Function to find sum of given seriesdef sumOfSeries(n):    return (n * (n + 1) * (2 * n + 4)) / 12;     # Driver functionif __name__ == '__main__':    n = 10    print(sumOfSeries(n))
// C# Code For Sum of the seriesusing 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 program to find// sum of given series // Function to find// sum of given seriesfunction sumOfSeries($n){    return ($n * ($n + 1) *           (2 * $n + 4)) / 12;} // Driver Code$n = 10;echo(sumOfSeries($n)); // This code is contributed by Ajit.?>
<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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