Sum of the first 752 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 752 square numbers, you ask? Here we will give you the formula to calculate the first 752 square numbers and then we will show you how to calculate the first 752 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 752 square numbers, we enter n = 752 into our formula to get this:

		752(752 + 1) × (2(752) + 1)
		6

First, calculate each section of the numerator: 752(752 + 1) equals 566256 and (2(752) + 1) equals 1505. Therefore, the problem above becomes this:

		566256 × 1505
		6

Next, we calculate 566256 times 1505 which equals 852215280. Now our problem looks like this:

		852215280
		6

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

852215280 ÷ 6 = 142035880

There you go. The sum of the first 752 square numbers is 142035880.

You may also be interested to know that if you list the first 752 square numbers 1, 2, 9, etc., the 752nd square number is 565504.

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