Sum of square of first n odd numbers

CServer Side ProgrammingProgramming

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