Sum of fifth powers of the first n natural numbers
Last Updated :
17 Oct, 2022
Write a program to find the sum of Fifth powers of the first n natural numbers 15 + 25+ 35 + 45+ …….+ n5 till n-th term.
Examples:
Input : 4
Output : 1300
15 + 25 + 35 + 45 = 1300
Input : 6
Output : 12201
15 + 25 + 35 + 45 + 55 + 65
Naive Approach :- In this Simple finding the fifth powers of the first n natural numbers is iterate a loop from 1 to n time. like suppose n=5. and store in sum variable.
(1*1*1*1*1)+(2*2*2*2*2)+(3*3*3*3*3)+(4*4*4*4*4) = 1300
C++
#include <bits/stdc++.h>
using namespace std;
long long int fifthPowerSum( int n)
{
long long int sum = 0;
for ( int i = 1; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
int main()
{
int n = 6;
cout << fifthPowerSum(n) << endl;
return 0;
}
|
Java
import java.io.*;
class GFG
{
static long fifthPowerSum( int n)
{
long sum = 0 ;
for ( int i = 1 ; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
public static void main(String args[])
{
int n = 6 ;
System.out.println(fifthPowerSum(n));
}
}
|
Python3
def fifthPowerSum(n) :
sm = 0
for i in range ( 1 , n + 1 ) :
sm = sm + (i * i * i * i * i)
return sm
n = 6
print (fifthPowerSum(n))
|
C#
using System;
class GFG
{
static long fifthPowerSum( int n)
{
long sum = 0;
for ( int i = 1; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
public static void Main()
{
int n = 6;
Console.Write(fifthPowerSum(n));
}
}
|
PHP
<?php
function fifthPowerSum( $n )
{
$sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum = $sum + ( $i * $i * $i *
$i * $i );
return $sum ;
}
$n = 6;
echo (fifthPowerSum( $n ));
?>
|
Javascript
<script>
function fifthPowerSum( n)
{
let sum = 0;
for (let i = 1; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
let n = 6;
document.write(fifthPowerSum(n));
</script>
|
Time complexity: O(N)
Auxiliary Space: O(1)
Efficient Approach :- An efficient solution is to use direct mathematical formula which is :
(2*n6+6*n5+5*n4 - n2)/12
OR (Can also be written as)
(1/6)n6 + (1/2)n5 + (5/12)n4 – (1/12)n2.
C++
#include <bits/stdc++.h>
using namespace std;
long long int fifthPowerSum( int n)
{
return ((2 * n * n * n * n * n * n) +
(6 * n * n * n * n * n) +
(5 * n * n * n * n) -
(n * n)) / 12;
}
int main()
{
int n = 5;
cout << fifthPowerSum(n) << endl;
return 0;
}
|
Java
import java.io.*;
class GFG {
static long fifthPowerSum( int n)
{
return (( 2 * n * n * n * n * n * n) +
( 6 * n * n * n * n * n) +
( 5 * n * n * n * n) -
(n * n)) / 12 ;
}
public static void main(String args[])
{
int n = 5 ;
System.out.println(fifthPowerSum(n));
}
}
|
Python3
def fifthPowerSum(n) :
return (( 2 * n * n * n * n * n * n) +
( 6 * n * n * n * n * n) +
( 5 * n * n * n * n) -
(n * n)) / / 12
n = 5
print (fifthPowerSum(n))
|
C#
using System;
class GFG {
static long fifthPowerSum( int n)
{
return ((2 * n * n * n * n * n * n) +
(6 * n * n * n * n * n) +
(5 * n * n * n * n) -
(n * n)) / 12;
}
public static void Main()
{
int n = 5;
Console.Write(fifthPowerSum(n));
}
}
|
PHP
<?php
function fifthPowerSum( $n )
{
return ((2 * $n * $n * $n * $n * $n * $n ) +
(6 * $n * $n * $n * $n * $n ) +
(5 * $n * $n * $n * $n ) -
( $n * $n )) / 12;
}
$n = 5;
echo (fifthPowerSum( $n ));
?>
|
Javascript
<script>
function fifthPowerSum(n)
{
return ((2 * n * n * n * n * n * n) +
(6 * n * n * n * n * n) +
(5 * n * n * n * n) -
(n * n)) / 12;
}
let n = 5;
document.write(fifthPowerSum(n) + "<br>" );
</script>
|
Time complexity: O(1)
Auxiliary Space: O(1)
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