Sum of the first 2008 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 2008 square numbers, you ask? Here we will give you the formula to calculate the first 2008 square numbers and then we will show you how to calculate the first 2008 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 2008 square numbers, we enter n = 2008 into our formula to get this:

		2008(2008 + 1) × (2(2008) + 1)
		6

First, calculate each section of the numerator: 2008(2008 + 1) equals 4034072 and (2(2008) + 1) equals 4017. Therefore, the problem above becomes this:

		4034072 × 4017
		6

Next, we calculate 4034072 times 4017 which equals 16204867224. Now our problem looks like this:

		16204867224
		6

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

16204867224 ÷ 6 = 2700811204

There you go. The sum of the first 2008 square numbers is 2700811204.

You may also be interested to know that if you list the first 2008 square numbers 1, 2, 9, etc., the 2008th square number is 4032064.

Sum of Square Numbers Calculator
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