Calculator Use

Sum of Consecutive Squares Calculator is a free online tool that displays the result of Sum of Consecutive Squares. This online Sum of Consecutive Squares Calculator tool performs the calculation faster, and it displays the result in a fraction of seconds.

The procedure to use the Sum of Consecutive Squares Calculator is as follows:

Step 1: Enter a values in the input field

Step 2: Now click the "Calculate" button to get the result

Step 3: Finally, The result of Sum of Consecutive Squares will be displayed in the output field

What is Sum of Squares of n Natural Numbers?

The sum of n natural numbers is represented as 1 + 2 + 3 + 4 + ... + n = [n(n+1)]/2. If we need to calculate the sum of squares of n consecutive natural numbers, the formula is 1² + 2² + 3² + 4²...+ n² = Σn² = [n(n+1)(2n+1)] / 6.

Solved Examples:

Calaulate the sum of squares of first 20 natural numbers.

20 * (20 + 1) * (2 * 20 + 1) / 6

= 20 * 21 * 41 / 6

= 17220 / 6

= 2870

Calaulate the sum of squares of natural numbers from 10 to 25.

There are 25 integers between 1 and 25, and 9 integers less than 10. So, the sum of squares of natural numbers from 10 to 25 is

25 * (25 + 1) * (2 * 25 + 1) / 6 – 9 * (9 + 1) * (2 * 9 + 1) / 6

= 25 * 26 * 51 / 6 – 9 * 10 * 19 / 6

= 33150 / 6 – 1710 / 6

= 5525 – 285

= 5240

Sum of squares of first N even numbers formula

2 * N * (N + 1) * (2 * N + 1) / 3

Sum of squares of first N odd numbers formula

N * (2 * N + 1) * (2 * N – 1) / 3