Sum of the first 442 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 442 square numbers, you ask? Here we will give you the formula to calculate the first 442 square numbers and then we will show you how to calculate the first 442 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 442 square numbers, we enter n = 442 into our formula to get this:

		442(442 + 1) × (2(442) + 1)
		6

First, calculate each section of the numerator: 442(442 + 1) equals 195806 and (2(442) + 1) equals 885. Therefore, the problem above becomes this:

		195806 × 885
		6

Next, we calculate 195806 times 885 which equals 173288310. Now our problem looks like this:

		173288310
		6

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

173288310 ÷ 6 = 28881385

There you go. The sum of the first 442 square numbers is 28881385.

You may also be interested to know that if you list the first 442 square numbers 1, 2, 9, etc., the 442nd square number is 195364.

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