Sum of the first 122 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 122 square numbers, you ask? Here we will give you the formula to calculate the first 122 square numbers and then we will show you how to calculate the first 122 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 122 square numbers, we enter n = 122 into our formula to get this:

		122(122 + 1) × (2(122) + 1)
		6

First, calculate each section of the numerator: 122(122 + 1) equals 15006 and (2(122) + 1) equals 245. Therefore, the problem above becomes this:

		15006 × 245
		6

Next, we calculate 15006 times 245 which equals 3676470. Now our problem looks like this:

		3676470
		6

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

3676470 ÷ 6 = 612745

There you go. The sum of the first 122 square numbers is 612745.

You may also be interested to know that if you list the first 122 square numbers 1, 2, 9, etc., the 122nd square number is 14884.

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