Sum of the first 138 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 138 square numbers, you ask? Here we will give you the formula to calculate the first 138 square numbers and then we will show you how to calculate the first 138 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 138 square numbers, we enter n = 138 into our formula to get this:

		138(138 + 1) × (2(138) + 1)
		6

First, calculate each section of the numerator: 138(138 + 1) equals 19182 and (2(138) + 1) equals 277. Therefore, the problem above becomes this:

		19182 × 277
		6

Next, we calculate 19182 times 277 which equals 5313414. Now our problem looks like this:

		5313414
		6

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

5313414 ÷ 6 = 885569

There you go. The sum of the first 138 square numbers is 885569.

You may also be interested to know that if you list the first 138 square numbers 1, 2, 9, etc., the 138th square number is 19044.

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