Sum of the first 743 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 743 square numbers, you ask? Here we will give you the formula to calculate the first 743 square numbers and then we will show you how to calculate the first 743 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 743 square numbers, we enter n = 743 into our formula to get this:

		743(743 + 1) × (2(743) + 1)
		6

First, calculate each section of the numerator: 743(743 + 1) equals 552792 and (2(743) + 1) equals 1487. Therefore, the problem above becomes this:

		552792 × 1487
		6

Next, we calculate 552792 times 1487 which equals 822001704. Now our problem looks like this:

		822001704
		6

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

822001704 ÷ 6 = 137000284

There you go. The sum of the first 743 square numbers is 137000284.

You may also be interested to know that if you list the first 743 square numbers 1, 2, 9, etc., the 743rd square number is 552049.

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