Sum of the first 1002 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 1002 square numbers, you ask? Here we will give you the formula to calculate the first 1002 square numbers and then we will show you how to calculate the first 1002 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 1002 square numbers, we enter n = 1002 into our formula to get this:

		1002(1002 + 1) × (2(1002) + 1)
		6

First, calculate each section of the numerator: 1002(1002 + 1) equals 1005006 and (2(1002) + 1) equals 2005. Therefore, the problem above becomes this:

		1005006 × 2005
		6

Next, we calculate 1005006 times 2005 which equals 2015037030. Now our problem looks like this:

		2015037030
		6

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

2015037030 ÷ 6 = 335839505

There you go. The sum of the first 1002 square numbers is 335839505.

You may also be interested to know that if you list the first 1002 square numbers 1, 2, 9, etc., the 1002nd square number is 1004004.

Sum of Square Numbers Calculator
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