Sum of the first 494 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 494 square numbers, you ask? Here we will give you the formula to calculate the first 494 square numbers and then we will show you how to calculate the first 494 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 494 square numbers, we enter n = 494 into our formula to get this:

		494(494 + 1) × (2(494) + 1)
		6

First, calculate each section of the numerator: 494(494 + 1) equals 244530 and (2(494) + 1) equals 989. Therefore, the problem above becomes this:

		244530 × 989
		6

Next, we calculate 244530 times 989 which equals 241840170. Now our problem looks like this:

		241840170
		6

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

241840170 ÷ 6 = 40306695

There you go. The sum of the first 494 square numbers is 40306695.

You may also be interested to know that if you list the first 494 square numbers 1, 2, 9, etc., the 494th square number is 244036.

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