Sum of the first 2002 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 2002 square numbers, you ask? Here we will give you the formula to calculate the first 2002 square numbers and then we will show you how to calculate the first 2002 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 2002 square numbers, we enter n = 2002 into our formula to get this:

		2002(2002 + 1) × (2(2002) + 1)
		6

First, calculate each section of the numerator: 2002(2002 + 1) equals 4010006 and (2(2002) + 1) equals 4005. Therefore, the problem above becomes this:

		4010006 × 4005
		6

Next, we calculate 4010006 times 4005 which equals 16060074030. Now our problem looks like this:

		16060074030
		6

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

16060074030 ÷ 6 = 2676679005

There you go. The sum of the first 2002 square numbers is 2676679005.

You may also be interested to know that if you list the first 2002 square numbers 1, 2, 9, etc., the 2002nd square number is 4008004.

Sum of Square Numbers Calculator
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