Sum of the first 368 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 368 square numbers, you ask? Here we will give you the formula to calculate the first 368 square numbers and then we will show you how to calculate the first 368 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 368 square numbers, we enter n = 368 into our formula to get this:

		368(368 + 1) × (2(368) + 1)
		6

First, calculate each section of the numerator: 368(368 + 1) equals 135792 and (2(368) + 1) equals 737. Therefore, the problem above becomes this:

		135792 × 737
		6

Next, we calculate 135792 times 737 which equals 100078704. Now our problem looks like this:

		100078704
		6

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

100078704 ÷ 6 = 16679784

There you go. The sum of the first 368 square numbers is 16679784.

You may also be interested to know that if you list the first 368 square numbers 1, 2, 9, etc., the 368th square number is 135424.

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What is the sum of the first 369 square numbers?
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