Sum of the first 298 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 298 square numbers, you ask? Here we will give you the formula to calculate the first 298 square numbers and then we will show you how to calculate the first 298 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 298 square numbers, we enter n = 298 into our formula to get this:

		298(298 + 1) × (2(298) + 1)
		6

First, calculate each section of the numerator: 298(298 + 1) equals 89102 and (2(298) + 1) equals 597. Therefore, the problem above becomes this:

		89102 × 597
		6

Next, we calculate 89102 times 597 which equals 53193894. Now our problem looks like this:

		53193894
		6

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

53193894 ÷ 6 = 8865649

There you go. The sum of the first 298 square numbers is 8865649.

You may also be interested to know that if you list the first 298 square numbers 1, 2, 9, etc., the 298th square number is 88804.

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