Sum of the first 1372 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 1372 square numbers, you ask? Here we will give you the formula to calculate the first 1372 square numbers and then we will show you how to calculate the first 1372 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 1372 square numbers, we enter n = 1372 into our formula to get this:

		1372(1372 + 1) × (2(1372) + 1)
		6

First, calculate each section of the numerator: 1372(1372 + 1) equals 1883756 and (2(1372) + 1) equals 2745. Therefore, the problem above becomes this:

		1883756 × 2745
		6

Next, we calculate 1883756 times 2745 which equals 5170910220. Now our problem looks like this:

		5170910220
		6

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

5170910220 ÷ 6 = 861818370

There you go. The sum of the first 1372 square numbers is 861818370.

You may also be interested to know that if you list the first 1372 square numbers 1, 2, 9, etc., the 1372nd square number is 1882384.

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