Sum of the first 1299 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 1299 square numbers, you ask? Here we will give you the formula to calculate the first 1299 square numbers and then we will show you how to calculate the first 1299 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 1299 square numbers, we enter n = 1299 into our formula to get this:

		1299(1299 + 1) × (2(1299) + 1)
		6

First, calculate each section of the numerator: 1299(1299 + 1) equals 1688700 and (2(1299) + 1) equals 2599. Therefore, the problem above becomes this:

		1688700 × 2599
		6

Next, we calculate 1688700 times 2599 which equals 4388931300. Now our problem looks like this:

		4388931300
		6

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

4388931300 ÷ 6 = 731488550

There you go. The sum of the first 1299 square numbers is 731488550.

You may also be interested to know that if you list the first 1299 square numbers 1, 2, 9, etc., the 1299th square number is 1687401.

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