Sum of the first 1473 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 1473 square numbers, you ask? Here we will give you the formula to calculate the first 1473 square numbers and then we will show you how to calculate the first 1473 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 1473 square numbers, we enter n = 1473 into our formula to get this:

		1473(1473 + 1) × (2(1473) + 1)
		6

First, calculate each section of the numerator: 1473(1473 + 1) equals 2171202 and (2(1473) + 1) equals 2947. Therefore, the problem above becomes this:

		2171202 × 2947
		6

Next, we calculate 2171202 times 2947 which equals 6398532294. Now our problem looks like this:

		6398532294
		6

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

6398532294 ÷ 6 = 1066422049

There you go. The sum of the first 1473 square numbers is 1066422049.

You may also be interested to know that if you list the first 1473 square numbers 1, 2, 9, etc., the 1473rd square number is 2169729.

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