Sum of the first 1250 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 1250 square numbers, you ask? Here we will give you the formula to calculate the first 1250 square numbers and then we will show you how to calculate the first 1250 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 1250 square numbers, we enter n = 1250 into our formula to get this:

		1250(1250 + 1) × (2(1250) + 1)
		6

First, calculate each section of the numerator: 1250(1250 + 1) equals 1563750 and (2(1250) + 1) equals 2501. Therefore, the problem above becomes this:

		1563750 × 2501
		6

Next, we calculate 1563750 times 2501 which equals 3910938750. Now our problem looks like this:

		3910938750
		6

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

3910938750 ÷ 6 = 651823125

There you go. The sum of the first 1250 square numbers is 651823125.

You may also be interested to know that if you list the first 1250 square numbers 1, 2, 9, etc., the 1250th square number is 1562500.

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