Sum of the first 261 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 261 square numbers, you ask? Here we will give you the formula to calculate the first 261 square numbers and then we will show you how to calculate the first 261 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 261 square numbers, we enter n = 261 into our formula to get this:

		261(261 + 1) × (2(261) + 1)
		6

First, calculate each section of the numerator: 261(261 + 1) equals 68382 and (2(261) + 1) equals 523. Therefore, the problem above becomes this:

		68382 × 523
		6

Next, we calculate 68382 times 523 which equals 35763786. Now our problem looks like this:

		35763786
		6

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

35763786 ÷ 6 = 5960631

There you go. The sum of the first 261 square numbers is 5960631.

You may also be interested to know that if you list the first 261 square numbers 1, 2, 9, etc., the 261st square number is 68121.

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