Sum of the first 842 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 842 square numbers, you ask? Here we will give you the formula to calculate the first 842 square numbers and then we will show you how to calculate the first 842 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 842 square numbers, we enter n = 842 into our formula to get this:

		842(842 + 1) × (2(842) + 1)
		6

First, calculate each section of the numerator: 842(842 + 1) equals 709806 and (2(842) + 1) equals 1685. Therefore, the problem above becomes this:

		709806 × 1685
		6

Next, we calculate 709806 times 1685 which equals 1196023110. Now our problem looks like this:

		1196023110
		6

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

1196023110 ÷ 6 = 199337185

There you go. The sum of the first 842 square numbers is 199337185.

You may also be interested to know that if you list the first 842 square numbers 1, 2, 9, etc., the 842nd square number is 708964.

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