Sum of the first 1001 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 1001 square numbers, you ask? Here we will give you the formula to calculate the first 1001 square numbers and then we will show you how to calculate the first 1001 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 1001 square numbers, we enter n = 1001 into our formula to get this:

		1001(1001 + 1) × (2(1001) + 1)
		6

First, calculate each section of the numerator: 1001(1001 + 1) equals 1003002 and (2(1001) + 1) equals 2003. Therefore, the problem above becomes this:

		1003002 × 2003
		6

Next, we calculate 1003002 times 2003 which equals 2009013006. Now our problem looks like this:

		2009013006
		6

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

2009013006 ÷ 6 = 334835501

There you go. The sum of the first 1001 square numbers is 334835501.

You may also be interested to know that if you list the first 1001 square numbers 1, 2, 9, etc., the 1001st square number is 1002001.

Sum of Square Numbers Calculator
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