Sum of the first 1338 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 1338 square numbers, you ask? Here we will give you the formula to calculate the first 1338 square numbers and then we will show you how to calculate the first 1338 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 1338 square numbers, we enter n = 1338 into our formula to get this:

		1338(1338 + 1) × (2(1338) + 1)
		6

First, calculate each section of the numerator: 1338(1338 + 1) equals 1791582 and (2(1338) + 1) equals 2677. Therefore, the problem above becomes this:

		1791582 × 2677
		6

Next, we calculate 1791582 times 2677 which equals 4796065014. Now our problem looks like this:

		4796065014
		6

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

4796065014 ÷ 6 = 799344169

There you go. The sum of the first 1338 square numbers is 799344169.

You may also be interested to know that if you list the first 1338 square numbers 1, 2, 9, etc., the 1338th square number is 1790244.

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