Sum of the first 258 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 258 square numbers, you ask? Here we will give you the formula to calculate the first 258 square numbers and then we will show you how to calculate the first 258 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 258 square numbers, we enter n = 258 into our formula to get this:

		258(258 + 1) × (2(258) + 1)
		6

First, calculate each section of the numerator: 258(258 + 1) equals 66822 and (2(258) + 1) equals 517. Therefore, the problem above becomes this:

		66822 × 517
		6

Next, we calculate 66822 times 517 which equals 34546974. Now our problem looks like this:

		34546974
		6

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

34546974 ÷ 6 = 5757829

There you go. The sum of the first 258 square numbers is 5757829.

You may also be interested to know that if you list the first 258 square numbers 1, 2, 9, etc., the 258th square number is 66564.

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