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 <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
// 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
<?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?> |
Javascript
<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> |
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 <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
// 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 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 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// 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?> |
Javascript
<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> |
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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