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

23 Jun, 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
 
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++
Java
Python3
C#
PHP
Javascript
// C++ program to find sum of series// 1^2 - 2^2 + 3^3 - 4^4 + ... #include <bits/stdc++.h>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 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 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# 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// PHP program to find sum of series// 1^2 - 2^2 + 3^3 - 4^4 + ...// Function to find sum of seriesfunction sum_of_series($n){    $result = 0;    for ($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 $result;} // Driver Code // Get n$n = 3; // Find the sumecho sum_of_series($n),"\n"; // Get n$n = 10; // Find the sumecho sum_of_series($n),"\n"; // This Code is Contributed by anuj_67?>
<script> // javascript Program to find sum of series// 1^2 - 2^2 + 3^3 - 4^4 + ... // Function to find sum of seriesfunction sum_of_series(n){    var result = 0;    for (i = 1; i <= n; i++)    {         // If i is even        if (i % 2 == 0)            result = result -                    parseInt(Math.pow(i, 2));         // If i is odd        else            result = result +                    parseInt(Math.pow(i, 2));    }     // return the result    return result;} // Driver Code   // Get nvar n = 3; // Find the sumdocument.write(sum_of_series(n)+ "<br>"); // Get nn = 10; // Find the sumdocument.write(sum_of_series(n)); // This code is contributed by 29AjayKumar </script>
6
-55
 
 Time Complexity: O(nlogn)
Auxiliary Space: O(1)
It is based on condition of n If n is even: 
If n is odd:  
Below is the implementation of the above approach:  
C++
Java
Python3
C#
PHP
Javascript
// C++ Program to find sum of series// 1^2 - 2^2 +3^3 -4^4 + ... #include <bits/stdc++.h>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 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 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# 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// PHP program to find sum of series// 1^2 - 2^2 +3^3 -4^4 + ... // Function to find sum of seriesfunction 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 $result;} // Driver Code // Get n$n = 3; // Find the sumecho sum_of_series($n);echo ("\n"); // Get n$n = 10; // Find the sumecho sum_of_series($n);echo ("\n"); // Get n$n = 10; // This code is contributed// by Shivi_Aggarwal?>
<script>// Javascript Program to find sum of series// 1^2 - 2^2 +3^3 -4^4 + ...       // Function to find sum of series    function sum_of_series( n) {        let 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               // Get n        let n = 3;         // Find the sum        document.write(sum_of_series(n)+"<br/>");         // Get n        n = 10;         // Find the sum        document.write(sum_of_series(n)); // This code is contributed by 29AjayKumar </script>
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.
vt_m
Akanksha_Rai
Shivi_Aggarwal
ukasp
ankthon
29AjayKumar
samim2000
series
series-sum
Mathematical
School Programming
Mathematical
series
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