Sum of the first 467 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 467 square numbers, you ask? Here we will give you the formula to calculate the first 467 square numbers and then we will show you how to calculate the first 467 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 467 square numbers, we enter n = 467 into our formula to get this:

		467(467 + 1) × (2(467) + 1)
		6

First, calculate each section of the numerator: 467(467 + 1) equals 218556 and (2(467) + 1) equals 935. Therefore, the problem above becomes this:

		218556 × 935
		6

Next, we calculate 218556 times 935 which equals 204349860. Now our problem looks like this:

		204349860
		6

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

204349860 ÷ 6 = 34058310

There you go. The sum of the first 467 square numbers is 34058310.

You may also be interested to know that if you list the first 467 square numbers 1, 2, 9, etc., the 467th square number is 218089.

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