# Find Sum of Series 1^2 – 2^2 + 3^2 – 4^2 ….. upto n terms

Given a number n, the task is to find the sum of the below series upto n terms:

12 – 22 + 32 – 42 + …..

Examples:

Input: n = 2
Output: -3
Explanation:
sum = 12 - 22
= 1 - 4
= -3

Input: n = 3
Output: 6
Explanation:
sum = 12 - 22 + 32
= 1 - 4 + 9
= 6


### Naive Approach:

This method involves simply running a loop of i from 1 to n and if i is odd then simply add its square to the result it i is even then simply subtract square of it to the result.

Below is the implementation of the above approach:

## C++

 // C++ program to find sum of series  // 1^2 - 2^2 + 3^3 - 4^4 + ...     #include  using namespace std;     // Function to find sum of series  int sum_of_series(int n)  {      int result = 0;      for (int i = 1; i <= n; i++) {             // If i is even          if (i % 2 == 0)              result = result - pow(i, 2);             // If i is odd          else             result = result + pow(i, 2);      }         // return the result      return result;  }     // Driver Code  int main(void)  {         // Get n      int n = 3;         // Find the sum      cout << sum_of_series(n) << endl;         // Get n      n = 10;         // Find the sum      cout << sum_of_series(n) << endl;  }

## Java

 // Java Program to find sum of series  // 1^2 - 2^2 + 3^3 - 4^4 + ...  import java.util.*;  import java.lang.*;     class GFG  {  // Function to find sum of series  static int sum_of_series(int n)  {      int result = 0;      for (int i = 1; i <= n; i++)      {             // If i is even          if (i % 2 == 0)              result = result -                       (int)Math.pow(i, 2);             // If i is odd          else             result = result +                       (int)Math.pow(i, 2);      }         // return the result      return result;  }     // Driver Code  public static void main(String args[])  {         // Get n      int n = 3;         // Find the sum      System.out.println(sum_of_series(n));         // Get n      n = 10;         // Find the sum      System.out.println(sum_of_series(n));  }  }     // This code is contributed   // by Akanksha Rai(Abby_akku)

## Python3

 # Python3 program to find sum of series  # 1^2 - 2^2 + 3^3 - 4^4 + ...     # Function to find sum of series  def sum_of_series(n):         result = 0     for i in range(1, n + 1) :             # If i is even          if (i % 2 == 0):              result = result - pow(i, 2)             # If i is odd          else:              result = result + pow(i, 2)         # return the result      return result     # Driver Code  if __name__ == "__main__":         # Get n      n = 3        # Find the sum      print(sum_of_series(n))         # Get n      n = 10        # Find the sum      print(sum_of_series(n))     # This code is contributed   # by ChitraNayal

## C#

 // C# Program to find sum of series  // 1^2 - 2^2 + 3^3 - 4^4 + ...  using System;     class GFG  {  // Function to find sum of series  static int sum_of_series(int n)  {      int result = 0;      for (int i = 1; i <= n; i++)      {             // If i is even          if (i % 2 == 0)              result = result -                       (int)Math.Pow(i, 2);             // If i is odd          else             result = result +                       (int)Math.Pow(i, 2);      }         // return the result      return result;  }     // Driver Code  public static void Main()  {         // Get n      int n = 3;         // Find the sum      Console.WriteLine(sum_of_series(n));         // Get n      n = 10;         // Find the sum      Console.WriteLine(sum_of_series(n));  }  }     // This code is contributed   // by Akanksha Rai(Abby_akku)

## PHP

 

Output:

6
-55


Time Complexity: Complexity of above stated code is O(n).

### Efficient Approach

It is based on condition of n
If n is even:

If n is odd:

Below is the implementation of the above approach:

## C++

 // C++ Program to find sum of series  // 1^2 - 2^2 +3^3 -4^4 + ...     #include  using namespace std;     // Function to find sum of series  int sum_of_series(int n)  {      int result = 0;         // If n is even      if (n % 2 == 0) {          result = -(n * (n + 1)) / 2;      }         // If n is odd      else {          result = (n * (n + 1)) / 2;      }         // return the result      return result;  }     // Driver Code  int main(void)  {         // Get n      int n = 3;         // Find the sum      cout << sum_of_series(n) << endl;         // Get n      n = 10;         // Find the sum      cout << sum_of_series(n) << endl;  }

## Java

 // Java Program to find sum of series  // 1^2 - 2^2 +3^3 -4^4 + ...  import java.util.*;  import java.lang.*;     class GFG  {  // Function to find sum of series  static int sum_of_series(int n)  {      int result = 0;         // If n is even      if (n % 2 == 0)       {          result = -(n * (n + 1)) / 2;      }         // If n is odd      else     {          result = (n * (n + 1)) / 2;      }         // return the result      return result;  }     // Driver Code  public static void main(String args[])  {         // Get n      int n = 3;         // Find the sum      System.out.println(sum_of_series(n));         // Get n      n = 10;         // Find the sum      System.out.println(sum_of_series(n));  }  }     // This code is contributed   // by Akanksha Rai(Abby_akku)

## Python3

 # Python3 Program to find sum of series   # 1^2 - 2^2 +3^3 -4^4 + ...      # Function to find sum of series   def sum_of_series(n) :         result = 0        # If n is even       if (n % 2 == 0) :           result = -(n * (n + 1)) // 2            # If n is odd       else :          result = (n * (n + 1)) // 2            # return the result       return result     # Driver Code   if __name__ == "__main__" :         # Get n       n = 3        # Find the sum       print(sum_of_series(n))          # Get n       n = 10        # Find the sum       print(sum_of_series(n))      # This code is contributed by Ryuga

## C#

 // C# Program to find sum of series  // 1^2 - 2^2 +3^3 -4^4 + ...     using System;     class GFG  {  // Function to find sum of series  static int sum_of_series(int n)  {      int result = 0;         // If n is even      if (n % 2 == 0)       {          result = -(n * (n + 1)) / 2;      }         // If n is odd      else     {          result = (n * (n + 1)) / 2;      }         // return the result      return result;  }     // Driver Code  public static void Main()  {         // Get n      int n = 3;         // Find the sum      Console.WriteLine(sum_of_series(n));         // Get n      n = 10;         // Find the sum      Console.WriteLine(sum_of_series(n));  }  }     // This code is contributed   // by Akanksha Rai(Abby_akku)

## PHP

 

Output:

6
-55


My Personal Notes arrow_drop_up

Let the code do the talking

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