Sum of the first 472 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 472 square numbers, you ask? Here we will give you the formula to calculate the first 472 square numbers and then we will show you how to calculate the first 472 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 472 square numbers, we enter n = 472 into our formula to get this:

		472(472 + 1) × (2(472) + 1)
		6

First, calculate each section of the numerator: 472(472 + 1) equals 223256 and (2(472) + 1) equals 945. Therefore, the problem above becomes this:

		223256 × 945
		6

Next, we calculate 223256 times 945 which equals 210976920. Now our problem looks like this:

		210976920
		6

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

210976920 ÷ 6 = 35162820

There you go. The sum of the first 472 square numbers is 35162820.

You may also be interested to know that if you list the first 472 square numbers 1, 2, 9, etc., the 472nd square number is 222784.

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