Sum of the first 325 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 325 square numbers, you ask? Here we will give you the formula to calculate the first 325 square numbers and then we will show you how to calculate the first 325 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 325 square numbers, we enter n = 325 into our formula to get this:

		325(325 + 1) × (2(325) + 1)
		6

First, calculate each section of the numerator: 325(325 + 1) equals 105950 and (2(325) + 1) equals 651. Therefore, the problem above becomes this:

		105950 × 651
		6

Next, we calculate 105950 times 651 which equals 68973450. Now our problem looks like this:

		68973450
		6

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

68973450 ÷ 6 = 11495575

There you go. The sum of the first 325 square numbers is 11495575.

You may also be interested to know that if you list the first 325 square numbers 1, 2, 9, etc., the 325th square number is 105625.

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What is the sum of the first 326 square numbers?
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