Sum of the first 496 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 496 square numbers, you ask? Here we will give you the formula to calculate the first 496 square numbers and then we will show you how to calculate the first 496 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 496 square numbers, we enter n = 496 into our formula to get this:

		496(496 + 1) × (2(496) + 1)
		6

First, calculate each section of the numerator: 496(496 + 1) equals 246512 and (2(496) + 1) equals 993. Therefore, the problem above becomes this:

		246512 × 993
		6

Next, we calculate 246512 times 993 which equals 244786416. Now our problem looks like this:

		244786416
		6

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

244786416 ÷ 6 = 40797736

There you go. The sum of the first 496 square numbers is 40797736.

You may also be interested to know that if you list the first 496 square numbers 1, 2, 9, etc., the 496th square number is 246016.

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What is the sum of the first 497 square numbers?
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