Sum of the first 3742 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 3742 square numbers, you ask? Here we will give you the formula to calculate the first 3742 square numbers and then we will show you how to calculate the first 3742 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 3742 square numbers, we enter n = 3742 into our formula to get this:

		3742(3742 + 1) × (2(3742) + 1)
		6

First, calculate each section of the numerator: 3742(3742 + 1) equals 14006306 and (2(3742) + 1) equals 7485. Therefore, the problem above becomes this:

		14006306 × 7485
		6

Next, we calculate 14006306 times 7485 which equals 104837200410. Now our problem looks like this:

		104837200410
		6

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

104837200410 ÷ 6 = 17472866735

There you go. The sum of the first 3742 square numbers is 17472866735.

You may also be interested to know that if you list the first 3742 square numbers 1, 2, 9, etc., the 3742nd square number is 14002564.

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