Sum of the first 1317 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 1317 square numbers, you ask? Here we will give you the formula to calculate the first 1317 square numbers and then we will show you how to calculate the first 1317 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 1317 square numbers, we enter n = 1317 into our formula to get this:

		1317(1317 + 1) × (2(1317) + 1)
		6

First, calculate each section of the numerator: 1317(1317 + 1) equals 1735806 and (2(1317) + 1) equals 2635. Therefore, the problem above becomes this:

		1735806 × 2635
		6

Next, we calculate 1735806 times 2635 which equals 4573848810. Now our problem looks like this:

		4573848810
		6

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

4573848810 ÷ 6 = 762308135

There you go. The sum of the first 1317 square numbers is 762308135.

You may also be interested to know that if you list the first 1317 square numbers 1, 2, 9, etc., the 1317th square number is 1734489.

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