Sum of the first 4007 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 4007 square numbers, you ask? Here we will give you the formula to calculate the first 4007 square numbers and then we will show you how to calculate the first 4007 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 4007 square numbers, we enter n = 4007 into our formula to get this:

		4007(4007 + 1) × (2(4007) + 1)
		6

First, calculate each section of the numerator: 4007(4007 + 1) equals 16060056 and (2(4007) + 1) equals 8015. Therefore, the problem above becomes this:

		16060056 × 8015
		6

Next, we calculate 16060056 times 8015 which equals 128721348840. Now our problem looks like this:

		128721348840
		6

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

128721348840 ÷ 6 = 21453558140

There you go. The sum of the first 4007 square numbers is 21453558140.

You may also be interested to know that if you list the first 4007 square numbers 1, 2, 9, etc., the 4007th square number is 16056049.

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