Sum of the first 1321 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 1321 square numbers, you ask? Here we will give you the formula to calculate the first 1321 square numbers and then we will show you how to calculate the first 1321 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 1321 square numbers, we enter n = 1321 into our formula to get this:

		1321(1321 + 1) × (2(1321) + 1)
		6

First, calculate each section of the numerator: 1321(1321 + 1) equals 1746362 and (2(1321) + 1) equals 2643. Therefore, the problem above becomes this:

		1746362 × 2643
		6

Next, we calculate 1746362 times 2643 which equals 4615634766. Now our problem looks like this:

		4615634766
		6

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

4615634766 ÷ 6 = 769272461

There you go. The sum of the first 1321 square numbers is 769272461.

You may also be interested to know that if you list the first 1321 square numbers 1, 2, 9, etc., the 1321st square number is 1745041.

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