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 = 1300Input : 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
// CPP Program to find the sum of fifth powers // of first n natural numbers #include <bits/stdc++.h> using namespace std;
// calculate the sum of fifth power of // first n natural numbers 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;
} // Driven Program int main()
{ int n = 6;
cout << fifthPowerSum(n) << endl;
return 0;
} |
// Java Program to find the // sum of fifth powers of // first n natural numbers import java.io.*;
class GFG
{ // calculate the sum of fifth
// power of first n natural
// numbers
static long fifthPowerSum( int n)
{
long sum = 0 ;
for ( int i = 1 ; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
// Driven Program
public static void main(String args[])
{
int n = 6 ;
System.out.println(fifthPowerSum(n));
}
} // This code is contributed by // Nikita Tiwari. |
# Python 3 Program to find the # sum of fifth powers of first # n natural numbers # calculate the sum of fifth # power of first n natural # numbers def fifthPowerSum(n) :
sm = 0
for i in range ( 1 , n + 1 ) :
sm = sm + (i * i * i * i * i)
return sm
# Driven Program n = 6
print (fifthPowerSum(n))
# This code is contributed # by Nikita Tiwari. |
// C# Program to find the // sum of fifth powers of // first n natural numbers using System;
class GFG
{ // calculate the sum of fifth
// power of first n natural
// numbers
static long fifthPowerSum( int n)
{
long sum = 0;
for ( int i = 1; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
}
// Driven Program
public static void Main()
{
int n = 6;
Console.Write(fifthPowerSum(n));
}
} // This code is contributed by // vt_m. |
<?php // PHP Program to find // the sum of fifth powers // of first n natural numbers // calculate the sum of // fifth power of // first n natural numbers function fifthPowerSum( $n )
{ $sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum = $sum + ( $i * $i * $i *
$i * $i );
return $sum ;
} // Driver Code $n = 6;
echo (fifthPowerSum( $n ));
// This code is contributed by Ajit. ?> |
<script> // javascript Program to find the sum of fifth powers // of first n natural numbers // calculate the sum of fifth power of // first n natural numbers function fifthPowerSum( n)
{ let sum = 0;
for (let i = 1; i <= n; i++)
sum = sum + (i * i * i * i * i);
return sum;
} // Driven Program let n = 6;
document.write(fifthPowerSum(n));
// This code contributed by aashish1995 </script> |
12201
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.
// CPP Program to find the sum of fifth power // of first n natural numbers #include <bits/stdc++.h> using namespace std;
// calculate the sum of fifth power of first n natural numbers 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;
} // Driven Program int main()
{ int n = 5;
cout << fifthPowerSum(n) << endl;
return 0;
} |
// Java Program to find the sum of fifth power // of first n natural numbers import java.io.*;
class GFG {
// calculate the sum of fifth power
//of first n natural numbers
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 ;
}
// Driven Program
public static void main(String args[])
{
int n = 5 ;
System.out.println(fifthPowerSum(n));
}
} /*This code is contributed by Nikita Tiwari.*/
|
# Python 3 Program to find the # sum of fifth power of first # n natural numbers # Calculate the sum of fifth # power of first n natural # numbers 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
# Driven Program n = 5
print (fifthPowerSum(n))
# This code is contributed by Nikita Tiwari. |
// C# Program to find the sum // of fifth power of first n // natural numbers using System;
class GFG {
// calculate the sum of fifth power
// of first n natural numbers
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;
}
// Driven Program
public static void Main()
{
int n = 5;
Console.Write(fifthPowerSum(n));
}
} /*This code is contributed by vt_m.*/ |
<?php // PHP Program to find // the sum of fifth power // of first n natural numbers // calculate the sum of // fifth power of first // n natural numbers 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;
} // Driver Code $n = 5;
echo (fifthPowerSum( $n ));
// This code is contributed by Ajit. ?> |
<script> // JavaScript Program to find the sum of fifth power // of first n natural numbers // calculate the sum of fifth power of first n natural numbers 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;
} // Driven Program let n = 5;
document.write(fifthPowerSum(n) + "<br>" );
// This code is contributed by Mayank Tyagi </script> |
4425
Time complexity: O(1)
Auxiliary Space: O(1)