Sum of the first 40 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 40 square numbers, you ask? Here we will give you the formula to calculate the first 40 square numbers and then we will show you how to calculate the first 40 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 40 square numbers, we enter n = 40 into our formula to get this:

		40(40 + 1) × (2(40) + 1)
		6

First, calculate each section of the numerator: 40(40 + 1) equals 1640 and (2(40) + 1) equals 81. Therefore, the problem above becomes this:

		1640 × 81
		6

Next, we calculate 1640 times 81 which equals 132840. Now our problem looks like this:

		132840
		6

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

132840 ÷ 6 = 22140

There you go. The sum of the first 40 square numbers is 22140.

You may also be interested to know that if you list the first 40 square numbers 1, 2, 9, etc., the 40th square number is 1600.

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