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
C++
// 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 numberslong 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 Programint main(){ int n = 6; cout << fifthPowerSum(n) << endl; return 0;} |
Java
// Java Program to find the // sum of fifth powers of // first n natural numbersimport 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. |
Python3
# 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 # numbersdef fifthPowerSum(n) : sm = 0 for i in range(1, n+1) : sm = sm + (i * i * i * i * i) return sm# Driven Programn = 6print(fifthPowerSum(n))# This code is contributed # by Nikita Tiwari. |
C#
// C# Program to find the // sum of fifth powers of // first n natural numbersusing 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// PHP Program to find// the sum of fifth powers// of first n natural numbers// calculate the sum of// fifth power of// first n natural numbersfunction 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.?> |
Javascript
<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 numbersfunction 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> |
Output
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.
C++
// 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 numberslong 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 Programint main(){ int n = 5; cout << fifthPowerSum(n) << endl; return 0;} |
Java
// Java Program to find the sum of fifth power// of first n natural numbersimport 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.*/ |
Python3
# 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 # numbersdef 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 Programn = 5print(fifthPowerSum(n))# This code is contributed by Nikita Tiwari. |
C#
// C# Program to find the sum // of fifth power of first n // natural numbersusing 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// PHP Program to find // the sum of fifth power// of first n natural numbers// calculate the sum of// fifth power of first// n natural numbersfunction 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.?> |
Javascript
<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 numbersfunction 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> |
Output
4425
Time complexity: O(1)
Auxiliary Space: O(1)
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