Sum of the first 267 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 267 square numbers, you ask? Here we will give you the formula to calculate the first 267 square numbers and then we will show you how to calculate the first 267 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 267 square numbers, we enter n = 267 into our formula to get this:

		267(267 + 1) × (2(267) + 1)
		6

First, calculate each section of the numerator: 267(267 + 1) equals 71556 and (2(267) + 1) equals 535. Therefore, the problem above becomes this:

		71556 × 535
		6

Next, we calculate 71556 times 535 which equals 38282460. Now our problem looks like this:

		38282460
		6

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

38282460 ÷ 6 = 6380410

There you go. The sum of the first 267 square numbers is 6380410.

You may also be interested to know that if you list the first 267 square numbers 1, 2, 9, etc., the 267th square number is 71289.

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