Sum of the first 794 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 794 square numbers, you ask? Here we will give you the formula to calculate the first 794 square numbers and then we will show you how to calculate the first 794 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 794 square numbers, we enter n = 794 into our formula to get this:

		794(794 + 1) × (2(794) + 1)
		6

First, calculate each section of the numerator: 794(794 + 1) equals 631230 and (2(794) + 1) equals 1589. Therefore, the problem above becomes this:

		631230 × 1589
		6

Next, we calculate 631230 times 1589 which equals 1003024470. Now our problem looks like this:

		1003024470
		6

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

1003024470 ÷ 6 = 167170745

There you go. The sum of the first 794 square numbers is 167170745.

You may also be interested to know that if you list the first 794 square numbers 1, 2, 9, etc., the 794th square number is 630436.

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