Sum of the first 400 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 400 square numbers, you ask? Here we will give you the formula to calculate the first 400 square numbers and then we will show you how to calculate the first 400 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 400 square numbers, we enter n = 400 into our formula to get this:

		400(400 + 1) × (2(400) + 1)
		6

First, calculate each section of the numerator: 400(400 + 1) equals 160400 and (2(400) + 1) equals 801. Therefore, the problem above becomes this:

		160400 × 801
		6

Next, we calculate 160400 times 801 which equals 128480400. Now our problem looks like this:

		128480400
		6

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

128480400 ÷ 6 = 21413400

There you go. The sum of the first 400 square numbers is 21413400.

You may also be interested to know that if you list the first 400 square numbers 1, 2, 9, etc., the 400th square number is 160000.

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