# 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


## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

Naive Approach :
Below is implementation of above series :

## C++

 // CPP program to find sum of given series  #include  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

 

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  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

 

Output :

220


My Personal Notes arrow_drop_up Lets get started

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : jit_t