Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2
Given a series 12 + 32 + 52 + 72 + . . . + (2*n – 1)2, find sum of the series.
Examples:
Input : n = 4 Output : 84 Explanation : sum = 12 + 32 + 52 + 72 = 1 + 9 + 25 + 49 = 84 Input : n = 10 Output : 1330 Explanation : sum = 12 + 32 + 52 + 72 + 92 + 112 + 132 + 152 + 172 + 192 = 1 + 9 + 24 + 49 + . . . + 361 = 1330
C++
// Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. #include <bits/stdc++.h> using namespace std; // Function to find sum of series. int sumOfSeries( int n) { int sum = 0; for ( int i = 1; i <= n; i++) sum = sum + (2 * i - 1) * (2 * i - 1); return sum; } // Driver code int main() { int n = 10; cout << sumOfSeries(n); return 0; } |
Java
// Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. import java.io.*; class GFG { // Function to find sum of series. static int sumOfSeries( int n) { int sum = 0 ; for ( int i = 1 ; i <= n; i++) sum = sum + ( 2 * i - 1 ) * ( 2 * i - 1 ); return sum; } // Driver code public static void main(String[] args) { int n = 10 ; System.out.println( sumOfSeries(n)); } } |
Python3
# Python Program to find sum of series # 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. import math # Function to find sum of series. def sumOfSeries(n): sum = 0 for i in range ( 1 ,n + 1 ): sum = sum + ( 2 * i - 1 ) * ( 2 * i - 1 ) return sum # driver code n = 10 print (sumOfSeries(n)) # This code is contributed by Gitanjali. |
C#
// C# Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. using System; class GFG { // Function to find sum of series. static int sumOfSeries( int n) { int sum = 0; for ( int i = 1; i <= n; i++) sum = sum + (2 * i - 1) * (2 * i - 1); return sum; } // Driver code public static void Main() { int n = 10; Console.Write( sumOfSeries(n)); } } /* This code is contributed by vt_m*/ |
PHP
<?php // PHP Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. // Function to find sum of series. function sumOfSeries( $n ) { $sum = 0; for ( $i = 1; $i <= $n ; $i ++) $sum = $sum + (2 * $i - 1) * (2 * $i - 1); return $sum ; } // Driver code $n = 10; echo (sumOfSeries( $n )); // This code is contributed by Ajit. ?> |
Javascript
<script> // JavaScript program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. // Function to find sum of series. function sumOfSeries(n) { let sum = 0; for (let i = 1; i <= n; i++) sum = sum + (2 * i - 1) * (2 * i - 1); return sum; } // Driver Code let n = 10; document.write(sumOfSeries(n)); // This code is contributed by avijitmondal1998 </script> |
Output:
1330
Time Complexity : O(n)
Auxiliary Space: O(1)
Another approach : Using formula to find sum of series :
12 + 32 + 52 + 72 + . . . + (2*n - 1)2 = (n * (2 * n - 1) * (2 * n + 1)) / 3. Please refer sum of squares of even and odd numbers for proof.
C++
// Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. #include <bits/stdc++.h> using namespace std; // Function that find sum of series. int sumOfSeries( int n) { // Formula to find sum of series. return (n * (2 * n - 1) * (2 * n + 1)) / 3; } // Driver code int main() { int n = 10; cout << sumOfSeries(n); return 0; } |
Java
// Java Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. import java.io.*; import java.util.*; class GFG { // Function to find sum of series. static int sumOfSeries( int n) { // Formula to find sum of series. return (n * ( 2 * n - 1 ) * ( 2 * n + 1 )) / 3 ; } // Driver function public static void main (String[] args) { int n= 10 ; System.out.println(sumOfSeries(n)); } } // This code is contributed by Gitanjali. |
Python3
# Python Program to find sum of series # 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. import math # Function to find sum of series. def sumOfSeries(n): # Formula to find sum of series. return int ((n * ( 2 * n - 1 ) * ( 2 * n + 1 )) / 3 ) # driver code n = 10 print (sumOfSeries(n)) # This code is contributed by Gitanjali. |
C#
// C# Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. using System; class GFG { // Function to find sum of series. static int sumOfSeries( int n) { // Formula to find sum of series. return (n * (2 * n - 1) * (2 * n + 1)) / 3; } // Driver function public static void Main () { int n = 10; Console.Write(sumOfSeries(n)); } } // This code is contributed by vt_m. |
PHP
<?php // PHP Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. // Function that find sum of series. function sumOfSeries( $n ) { // Formula to find sum of series. return ( $n * (2 * $n - 1) * (2 * $n + 1)) / 3; } // Driver code $n = 10; echo (sumOfSeries( $n )); // This code is contributed by Ajit. ?> |
Javascript
<script> // Javascript Program to find sum of series // 1^2 + 3^2 + 5^2 + . . . + (2*n - 1)^2. // Function that find sum of series. function sumOfSeries(n) { // Formula to find sum of series. return (n * (2 * n - 1) * (2 * n + 1)) / 3; } // Driver code let n = 10; document.write(sumOfSeries(n)); // This code is contributed by _saurabh_jaiswal. </script> |
Output:
1330
Time Complexity: O(1)
Auxiliary space: O(1) since using constant variables
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