Sum of the first 804 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 804 square numbers, you ask? Here we will give you the formula to calculate the first 804 square numbers and then we will show you how to calculate the first 804 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 804 square numbers, we enter n = 804 into our formula to get this:

		804(804 + 1) × (2(804) + 1)
		6

First, calculate each section of the numerator: 804(804 + 1) equals 647220 and (2(804) + 1) equals 1609. Therefore, the problem above becomes this:

		647220 × 1609
		6

Next, we calculate 647220 times 1609 which equals 1041376980. Now our problem looks like this:

		1041376980
		6

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

1041376980 ÷ 6 = 173562830

There you go. The sum of the first 804 square numbers is 173562830.

You may also be interested to know that if you list the first 804 square numbers 1, 2, 9, etc., the 804th square number is 646416.

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