Sum of the first 21 square numbers

We define square numbers as numbers that when squared will equal a whole number. Thus, the list of the first square numbers starts with 1, 4, 9, 16, and so on.

What is the sum of the first 21 square numbers, you ask? Here we will give you the formula to calculate the first 21 square numbers and then we will show you how to calculate the first 21 square numbers using the formula.

The formula to calculate the first n square numbers is displayed below:

		n(n + 1) × (2(n) + 1)
		6

To calculate the sum of the first 21 square numbers, we enter n = 21 into our formula to get this:

		21(21 + 1) × (2(21) + 1)
		6

First, calculate each section of the numerator: 21(21 + 1) equals 462 and (2(21) + 1) equals 43. Therefore, the problem above becomes this:

		462 × 43
		6

Next, we calculate 462 times 43 which equals 19866. Now our problem looks like this:

		19866
		6

Finally, divide the numerator by the denominator to get our answer:

19866 ÷ 6 = 3311

There you go. The sum of the first 21 square numbers is 3311.

You may also be interested to know that if you list the first 21 square numbers 1, 2, 9, etc., the 21st square number is 441.

Sum of Square Numbers Calculator
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