Sum of kth powers of first n natural numbers | Java program to find sum pf k - th powers of first n natural numbers . ; A global array to store factorials ; Function to calculate the factorials of all the numbers upto k ; Function to return the binomial coefficient ; nCr = ( n ! * ( n - r ) ! ) / r ! ; Function to return the sum of kth powers of n natural numbers ; When j is unity ; Calculating sum ( n ^ 1 ) of unity powers of n ; storing sum ( n ^ 1 ) for sum ( n ^ 2 ) ; If k = 1 then temp is the result ; For finding sum ( n ^ k ) removing 1 and n * kCk from ( n + 1 ) ^ k ; Removing all kC2 * sum ( n ^ ( k - 2 ) ) + ... + kCk - 1 * ( sum ( n ^ ( k - ( k - 1 ) ) ; Storing the result for next sum of next powers of k ; Driver code
import java . io . * ; class GFG { static int MAX_K = 15 ; static int fac [ ] = new int [ MAX_K ] ; static void factorial ( int k ) { fac [ 0 ] = 1 ; for ( int i = 1 ; i <= k + 1 ; i ++ ) { fac [ i ] = ( i * fac [ i - 1 ] ) ; } } static int bin ( int a , int b ) { int ans = ( ( fac [ a ] ) / ( fac [ a - b ] * fac [ b ] ) ) ; return ans ; } static int sumofn ( int n , int k ) { int p = 0 ; int num1 , temp ; int arr [ ] = new int [ 1000 ] ; for ( int j = 1 ; j <= k ; j ++ ) { if ( j == 1 ) { num1 = ( n * ( n + 1 ) ) / 2 ; arr [ p ++ ] = num1 ; temp = num1 ; } else { temp = ( ( int ) Math . pow ( n + 1 , j + 1 ) - 1 - n ) ; for ( int s = 1 ; s < j ; s ++ ) { temp = temp - ( arr [ j - s - 1 ] * bin ( j + 1 , s + 1 ) ) ; } temp = temp / ( j + 1 ) ; arr [ p ++ ] = temp ; } } temp = arr [ p - 1 ] ; return temp ; } public static void main ( String [ ] args ) { int n = 5 , k = 2 ; factorial ( k ) ; System . out . println ( sumofn ( n , k ) ) ; } }