Sum of the first 1442 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 1442 square numbers, you ask? Here we will give you the formula to calculate the first 1442 square numbers and then we will show you how to calculate the first 1442 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 1442 square numbers, we enter n = 1442 into our formula to get this:

		1442(1442 + 1) × (2(1442) + 1)
		6

First, calculate each section of the numerator: 1442(1442 + 1) equals 2080806 and (2(1442) + 1) equals 2885. Therefore, the problem above becomes this:

		2080806 × 2885
		6

Next, we calculate 2080806 times 2885 which equals 6003125310. Now our problem looks like this:

		6003125310
		6

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

6003125310 ÷ 6 = 1000520885

There you go. The sum of the first 1442 square numbers is 1000520885.

You may also be interested to know that if you list the first 1442 square numbers 1, 2, 9, etc., the 1442nd square number is 2079364.

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