Sum of the first 624 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 624 square numbers, you ask? Here we will give you the formula to calculate the first 624 square numbers and then we will show you how to calculate the first 624 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 624 square numbers, we enter n = 624 into our formula to get this:

		624(624 + 1) × (2(624) + 1)
		6

First, calculate each section of the numerator: 624(624 + 1) equals 390000 and (2(624) + 1) equals 1249. Therefore, the problem above becomes this:

		390000 × 1249
		6

Next, we calculate 390000 times 1249 which equals 487110000. Now our problem looks like this:

		487110000
		6

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

487110000 ÷ 6 = 81185000

There you go. The sum of the first 624 square numbers is 81185000.

You may also be interested to know that if you list the first 624 square numbers 1, 2, 9, etc., the 624th square number is 389376.

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What is the sum of the first 625 square numbers?
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