Sum of the first 1251 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 1251 square numbers, you ask? Here we will give you the formula to calculate the first 1251 square numbers and then we will show you how to calculate the first 1251 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 1251 square numbers, we enter n = 1251 into our formula to get this:

		1251(1251 + 1) × (2(1251) + 1)
		6

First, calculate each section of the numerator: 1251(1251 + 1) equals 1566252 and (2(1251) + 1) equals 2503. Therefore, the problem above becomes this:

		1566252 × 2503
		6

Next, we calculate 1566252 times 2503 which equals 3920328756. Now our problem looks like this:

		3920328756
		6

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

3920328756 ÷ 6 = 653388126

There you go. The sum of the first 1251 square numbers is 653388126.

You may also be interested to know that if you list the first 1251 square numbers 1, 2, 9, etc., the 1251st square number is 1565001.

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