Sum of the first 721 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 721 square numbers, you ask? Here we will give you the formula to calculate the first 721 square numbers and then we will show you how to calculate the first 721 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 721 square numbers, we enter n = 721 into our formula to get this:

		721(721 + 1) × (2(721) + 1)
		6

First, calculate each section of the numerator: 721(721 + 1) equals 520562 and (2(721) + 1) equals 1443. Therefore, the problem above becomes this:

		520562 × 1443
		6

Next, we calculate 520562 times 1443 which equals 751170966. Now our problem looks like this:

		751170966
		6

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

751170966 ÷ 6 = 125195161

There you go. The sum of the first 721 square numbers is 125195161.

You may also be interested to know that if you list the first 721 square numbers 1, 2, 9, etc., the 721st square number is 519841.

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