# 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 seriesint 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 Codeint 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 seriesstatic 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 Codepublic 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 seriesdef 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 Codeif __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 seriesstatic 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 Codepublic 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 seriesint 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 Codeint 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 seriesstatic 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 Codepublic 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 seriesdef 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 Codeif __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 seriesstatic 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 Codepublic 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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