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.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
… [Trackback]
[…] Read More to that Topic: geeksforgeeks.org/find-sum-of-series-1-2-2-2-3-2-4-2-upto-n-terms/ […]
… [Trackback]
[…] Find More Info here on that Topic: geeksforgeeks.org/find-sum-of-series-1-2-2-2-3-2-4-2-upto-n-terms/ […]