Sum of the first 598 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 598 square numbers, you ask? Here we will give you the formula to calculate the first 598 square numbers and then we will show you how to calculate the first 598 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 598 square numbers, we enter n = 598 into our formula to get this:

		598(598 + 1) × (2(598) + 1)
		6

First, calculate each section of the numerator: 598(598 + 1) equals 358202 and (2(598) + 1) equals 1197. Therefore, the problem above becomes this:

		358202 × 1197
		6

Next, we calculate 358202 times 1197 which equals 428767794. Now our problem looks like this:

		428767794
		6

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

428767794 ÷ 6 = 71461299

There you go. The sum of the first 598 square numbers is 71461299.

You may also be interested to know that if you list the first 598 square numbers 1, 2, 9, etc., the 598th square number is 357604.

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