Sum of the first 123 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 123 square numbers, you ask? Here we will give you the formula to calculate the first 123 square numbers and then we will show you how to calculate the first 123 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 123 square numbers, we enter n = 123 into our formula to get this:

		123(123 + 1) × (2(123) + 1)
		6

First, calculate each section of the numerator: 123(123 + 1) equals 15252 and (2(123) + 1) equals 247. Therefore, the problem above becomes this:

		15252 × 247
		6

Next, we calculate 15252 times 247 which equals 3767244. Now our problem looks like this:

		3767244
		6

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

3767244 ÷ 6 = 627874

There you go. The sum of the first 123 square numbers is 627874.

You may also be interested to know that if you list the first 123 square numbers 1, 2, 9, etc., the 123rd square number is 15129.

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