Sum of the first 133 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 133 square numbers, you ask? Here we will give you the formula to calculate the first 133 square numbers and then we will show you how to calculate the first 133 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 133 square numbers, we enter n = 133 into our formula to get this:

		133(133 + 1) × (2(133) + 1)
		6

First, calculate each section of the numerator: 133(133 + 1) equals 17822 and (2(133) + 1) equals 267. Therefore, the problem above becomes this:

		17822 × 267
		6

Next, we calculate 17822 times 267 which equals 4758474. Now our problem looks like this:

		4758474
		6

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

4758474 ÷ 6 = 793079

There you go. The sum of the first 133 square numbers is 793079.

You may also be interested to know that if you list the first 133 square numbers 1, 2, 9, etc., the 133rd square number is 17689.

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