Sum of the first 3375 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 3375 square numbers, you ask? Here we will give you the formula to calculate the first 3375 square numbers and then we will show you how to calculate the first 3375 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 3375 square numbers, we enter n = 3375 into our formula to get this:

		3375(3375 + 1) × (2(3375) + 1)
		6

First, calculate each section of the numerator: 3375(3375 + 1) equals 11394000 and (2(3375) + 1) equals 6751. Therefore, the problem above becomes this:

		11394000 × 6751
		6

Next, we calculate 11394000 times 6751 which equals 76920894000. Now our problem looks like this:

		76920894000
		6

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

76920894000 ÷ 6 = 12820149000

There you go. The sum of the first 3375 square numbers is 12820149000.

You may also be interested to know that if you list the first 3375 square numbers 1, 2, 9, etc., the 3375th square number is 11390625.

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