Sum of the first 272 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 272 square numbers, you ask? Here we will give you the formula to calculate the first 272 square numbers and then we will show you how to calculate the first 272 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 272 square numbers, we enter n = 272 into our formula to get this:

		272(272 + 1) × (2(272) + 1)
		6

First, calculate each section of the numerator: 272(272 + 1) equals 74256 and (2(272) + 1) equals 545. Therefore, the problem above becomes this:

		74256 × 545
		6

Next, we calculate 74256 times 545 which equals 40469520. Now our problem looks like this:

		40469520
		6

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

40469520 ÷ 6 = 6744920

There you go. The sum of the first 272 square numbers is 6744920.

You may also be interested to know that if you list the first 272 square numbers 1, 2, 9, etc., the 272nd square number is 73984.

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