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

• Last Updated : 25 Aug, 2022

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

 

## Javascript

 

Output:

6
-55

Time Complexity: O(n)

Auxiliary Space: O(1)

### 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

 

## Javascript

 

Output:

6
-55

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.

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