Sum of the first 38 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 38 square numbers, you ask? Here we will give you the formula to calculate the first 38 square numbers and then we will show you how to calculate the first 38 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 38 square numbers, we enter n = 38 into our formula to get this:

		38(38 + 1) × (2(38) + 1)
		6

First, calculate each section of the numerator: 38(38 + 1) equals 1482 and (2(38) + 1) equals 77. Therefore, the problem above becomes this:

		1482 × 77
		6

Next, we calculate 1482 times 77 which equals 114114. Now our problem looks like this:

		114114
		6

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

114114 ÷ 6 = 19019

There you go. The sum of the first 38 square numbers is 19019.

You may also be interested to know that if you list the first 38 square numbers 1, 2, 9, etc., the 38th square number is 1444.

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