Sum of the first 688 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 688 square numbers, you ask? Here we will give you the formula to calculate the first 688 square numbers and then we will show you how to calculate the first 688 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 688 square numbers, we enter n = 688 into our formula to get this:

		688(688 + 1) × (2(688) + 1)
		6

First, calculate each section of the numerator: 688(688 + 1) equals 474032 and (2(688) + 1) equals 1377. Therefore, the problem above becomes this:

		474032 × 1377
		6

Next, we calculate 474032 times 1377 which equals 652742064. Now our problem looks like this:

		652742064
		6

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

652742064 ÷ 6 = 108790344

There you go. The sum of the first 688 square numbers is 108790344.

You may also be interested to know that if you list the first 688 square numbers 1, 2, 9, etc., the 688th square number is 473344.

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