Sum of the first 502 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 502 square numbers, you ask? Here we will give you the formula to calculate the first 502 square numbers and then we will show you how to calculate the first 502 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 502 square numbers, we enter n = 502 into our formula to get this:

		502(502 + 1) × (2(502) + 1)
		6

First, calculate each section of the numerator: 502(502 + 1) equals 252506 and (2(502) + 1) equals 1005. Therefore, the problem above becomes this:

		252506 × 1005
		6

Next, we calculate 252506 times 1005 which equals 253768530. Now our problem looks like this:

		253768530
		6

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

253768530 ÷ 6 = 42294755

There you go. The sum of the first 502 square numbers is 42294755.

You may also be interested to know that if you list the first 502 square numbers 1, 2, 9, etc., the 502nd square number is 252004.

Sum of Square Numbers Calculator
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