Sum of the first 244 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 244 square numbers, you ask? Here we will give you the formula to calculate the first 244 square numbers and then we will show you how to calculate the first 244 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 244 square numbers, we enter n = 244 into our formula to get this:

		244(244 + 1) × (2(244) + 1)
		6

First, calculate each section of the numerator: 244(244 + 1) equals 59780 and (2(244) + 1) equals 489. Therefore, the problem above becomes this:

		59780 × 489
		6

Next, we calculate 59780 times 489 which equals 29232420. Now our problem looks like this:

		29232420
		6

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

29232420 ÷ 6 = 4872070

There you go. The sum of the first 244 square numbers is 4872070.

You may also be interested to know that if you list the first 244 square numbers 1, 2, 9, etc., the 244th square number is 59536.

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