Sum of the first 1264 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 1264 square numbers, you ask? Here we will give you the formula to calculate the first 1264 square numbers and then we will show you how to calculate the first 1264 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 1264 square numbers, we enter n = 1264 into our formula to get this:

		1264(1264 + 1) × (2(1264) + 1)
		6

First, calculate each section of the numerator: 1264(1264 + 1) equals 1598960 and (2(1264) + 1) equals 2529. Therefore, the problem above becomes this:

		1598960 × 2529
		6

Next, we calculate 1598960 times 2529 which equals 4043769840. Now our problem looks like this:

		4043769840
		6

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

4043769840 ÷ 6 = 673961640

There you go. The sum of the first 1264 square numbers is 673961640.

You may also be interested to know that if you list the first 1264 square numbers 1, 2, 9, etc., the 1264th square number is 1597696.

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