Sum of square of first n odd numbers

The series of squares of first n odd numbers takes squares of of first n odd numbers in series.

The series is: 1,9,25,49,81,121…

The series can also be written as − 1², 3², 5², 7², 9², 11²….

The sum of this series has a mathematical formula −

n(2n+1)(2n-1)/ 3= n(4n² - 1)/3

Lets take an example,

Input: N = 4
Output: sum =

Explanation

12 + 3² + 5² + 7² = 1 +9+ 25 + 49 = 84

Using formula, sum = 4(4(4)²- 1)/3 = 4(64-1)/3 = 4(63)/3 = 4*21 = 84 both these methods are good but the one using mathematical formula is better because it does not use looks which reduces its time complexity.

Example

#include <stdio.h>
int main() {
   int n = 8;
   int sum = 0;
   for (int i = 1; i <= n; i++)
      sum += (2*i - 1) * (2*i - 1);
   printf("The sum of square of first %d odd numbers is %d",n, sum);
   return 0;
}

Output

The sum of square of first 8 odd numbers is 680

Example

#include <stdio.h>
int main() {
   int n = 18;
   int sum = ((n*((4*n*n)-1))/3);
   printf("The sum of square of first %d odd numbers is %d",n, sum);
   return 0;
}

Output

The sum of square of first 18 odd numbers is 7770

Sudhir sharma

Published on 19-Aug-2019 12:10:00