Sum of series 1^2 + 3^2 + 5^2 + . . . + (2*n – 1)^2
Last Updated :
15 Jun, 2022
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++
#include <bits/stdc++.h>
using namespace std;
int sumOfSeries( int n)
{
int sum = 0;
for ( int i = 1; i <= n; i++)
sum = sum + (2 * i - 1) * (2 * i - 1);
return sum;
}
int main()
{
int n = 10;
cout << sumOfSeries(n);
return 0;
}
|
Java
import java.io.*;
class GFG {
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;
}
public static void main(String[] args)
{
int n = 10 ;
System.out.println( sumOfSeries(n));
}
}
|
Python3
import math
def sumOfSeries(n):
sum = 0
for i in range ( 1 ,n + 1 ):
sum = sum + ( 2 * i - 1 ) * ( 2 * i - 1 )
return sum
n = 10
print (sumOfSeries(n))
|
C#
using System;
class GFG {
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;
}
public static void Main()
{
int n = 10;
Console.Write( sumOfSeries(n));
}
}
|
PHP
<?php
function sumOfSeries( $n )
{
$sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum = $sum + (2 * $i - 1) *
(2 * $i - 1);
return $sum ;
}
$n = 10;
echo (sumOfSeries( $n ));
?>
|
Javascript
<script>
function sumOfSeries(n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum = sum + (2 * i - 1) *
(2 * i - 1);
return sum;
}
let n = 10;
document.write(sumOfSeries(n));
</script>
|
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++
#include <bits/stdc++.h>
using namespace std;
int sumOfSeries( int n)
{
return (n * (2 * n - 1) * (2 * n + 1)) / 3;
}
int main()
{
int n = 10;
cout << sumOfSeries(n);
return 0;
}
|
Java
import java.io.*;
import java.util.*;
class GFG {
static int sumOfSeries( int n)
{
return (n * ( 2 * n - 1 ) * ( 2 * n + 1 )) / 3 ;
}
public static void main (String[] args) {
int n= 10 ;
System.out.println(sumOfSeries(n));
}
}
|
Python3
import math
def sumOfSeries(n):
return int ((n * ( 2 * n - 1 ) * ( 2 * n + 1 )) / 3 )
n = 10
print (sumOfSeries(n))
|
C#
using System;
class GFG {
static int sumOfSeries( int n)
{
return (n * (2 * n - 1) * (2 * n + 1)) / 3;
}
public static void Main ()
{
int n = 10;
Console.Write(sumOfSeries(n));
}
}
|
PHP
<?php
function sumOfSeries( $n )
{
return ( $n * (2 * $n - 1) *
(2 * $n + 1)) / 3;
}
$n = 10;
echo (sumOfSeries( $n ));
?>
|
Javascript
<script>
function sumOfSeries(n)
{
return (n * (2 * n - 1) *
(2 * n + 1)) / 3;
}
let n = 10;
document.write(sumOfSeries(n));
</script>
|
Time Complexity: O(1)
Auxiliary space: O(1) since using constant variables
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