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Difference between sum of the squares of and square of sum first n natural numbers.
Problem Statement
With a given number n, write a program to find the difference between sum of the squares of and square of sum first n natural numbers.
Example
n = 3 Squares of first three numbers = 3x3 + 2x2 + 1x1 = 9 + 4 + 1 = 14 Squares of sum of first three numbers = (3 + 2 + 1)x(3 + 2 + 1) = 6x6 = 36 Difference = 36 - 14 = 22
Example
Following is the program in Java to find the required difference.
public class JavaTester {
public static int difference(int n){
//sum of squares of n natural numbers
int sumSquareN = (n * (n + 1) * (2 * n + 1)) / 6;
//sum of n natural numbers
int sumN = (n * (n + 1)) / 2;
//square of sum of n natural numbers
int squareSumN = sumN * sumN;
//difference
return Math.abs(sumSquareN - squareSumN);
}
public static void main(String args[]){
int n = 3;
System.out.println("Number: " + n);
System.out.println("Difference: " + difference(n));
}
}Output
Number : 3 Difference: 22
Updated on: 16-May-2020
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