Final answer:
To find the difference between the square of the sum and the sum of the squares of the first N natural numbers, we use the formulas for the sum of the first N natural numbers and the sum of the squares of the first N natural numbers. We substitute the values into the formula and calculate the result.
Step-by-step explanation:
To solve this problem, we need to calculate the square of the sum of the first N natural numbers and the sum of the squares of the first N natural numbers. Then, we subtract the sum of the squares from the square of the sum.We can use the formula for the sum of the first N natural numbers, which is (N * (N + 1)) / 2, and the formula for the sum of the squares of the first N natural numbers, which is (N * (N + 1) * (2N + 1)) / 6.Substituting the values into the formula, we get:(N * (N + 1) / 2)^2 - (N * (N + 1) * (2N + 1)) / 6For example, if N is 10, the calculation would be:((10 * 11) / 2)^2 - (10 * 11 * 21) / 6 = 2640.
The difference function calculates the difference between the square of the sum of the first N natural numbers and the sum of the squares of those numbers. To find the square of the sum, you can use the formula ∑i = n(n+1)/2, and then square the result. Whereas, the sum of the squares can be found using the formula ∑i² = n(n+1)(2n+1)/6. The difference is obtained by subtracting the latter from the former