Sum of the first 726 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 726 square numbers, you ask? Here we will give you the formula to calculate the first 726 square numbers and then we will show you how to calculate the first 726 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 726 square numbers, we enter n = 726 into our formula to get this:

		726(726 + 1) × (2(726) + 1)
		6

First, calculate each section of the numerator: 726(726 + 1) equals 527802 and (2(726) + 1) equals 1453. Therefore, the problem above becomes this:

		527802 × 1453
		6

Next, we calculate 527802 times 1453 which equals 766896306. Now our problem looks like this:

		766896306
		6

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

766896306 ÷ 6 = 127816051

There you go. The sum of the first 726 square numbers is 127816051.

You may also be interested to know that if you list the first 726 square numbers 1, 2, 9, etc., the 726th square number is 527076.

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