Sum of the first 476 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 476 square numbers, you ask? Here we will give you the formula to calculate the first 476 square numbers and then we will show you how to calculate the first 476 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 476 square numbers, we enter n = 476 into our formula to get this:

		476(476 + 1) × (2(476) + 1)
		6

First, calculate each section of the numerator: 476(476 + 1) equals 227052 and (2(476) + 1) equals 953. Therefore, the problem above becomes this:

		227052 × 953
		6

Next, we calculate 227052 times 953 which equals 216380556. Now our problem looks like this:

		216380556
		6

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

216380556 ÷ 6 = 36063426

There you go. The sum of the first 476 square numbers is 36063426.

You may also be interested to know that if you list the first 476 square numbers 1, 2, 9, etc., the 476th square number is 226576.

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