Sum of the first 337 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 337 square numbers, you ask? Here we will give you the formula to calculate the first 337 square numbers and then we will show you how to calculate the first 337 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 337 square numbers, we enter n = 337 into our formula to get this:

		337(337 + 1) × (2(337) + 1)
		6

First, calculate each section of the numerator: 337(337 + 1) equals 113906 and (2(337) + 1) equals 675. Therefore, the problem above becomes this:

		113906 × 675
		6

Next, we calculate 113906 times 675 which equals 76886550. Now our problem looks like this:

		76886550
		6

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

76886550 ÷ 6 = 12814425

There you go. The sum of the first 337 square numbers is 12814425.

You may also be interested to know that if you list the first 337 square numbers 1, 2, 9, etc., the 337th square number is 113569.

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