Sum of the first 462 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 462 square numbers, you ask? Here we will give you the formula to calculate the first 462 square numbers and then we will show you how to calculate the first 462 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 462 square numbers, we enter n = 462 into our formula to get this:

		462(462 + 1) × (2(462) + 1)
		6

First, calculate each section of the numerator: 462(462 + 1) equals 213906 and (2(462) + 1) equals 925. Therefore, the problem above becomes this:

		213906 × 925
		6

Next, we calculate 213906 times 925 which equals 197863050. Now our problem looks like this:

		197863050
		6

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

197863050 ÷ 6 = 32977175

There you go. The sum of the first 462 square numbers is 32977175.

You may also be interested to know that if you list the first 462 square numbers 1, 2, 9, etc., the 462nd square number is 213444.

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