Sum of the first 1502 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 1502 square numbers, you ask? Here we will give you the formula to calculate the first 1502 square numbers and then we will show you how to calculate the first 1502 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 1502 square numbers, we enter n = 1502 into our formula to get this:

		1502(1502 + 1) × (2(1502) + 1)
		6

First, calculate each section of the numerator: 1502(1502 + 1) equals 2257506 and (2(1502) + 1) equals 3005. Therefore, the problem above becomes this:

		2257506 × 3005
		6

Next, we calculate 2257506 times 3005 which equals 6783805530. Now our problem looks like this:

		6783805530
		6

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

6783805530 ÷ 6 = 1130634255

There you go. The sum of the first 1502 square numbers is 1130634255.

You may also be interested to know that if you list the first 1502 square numbers 1, 2, 9, etc., the 1502nd square number is 2256004.

Sum of Square Numbers Calculator
Need the answer to a similar problem? Get the first n square numbers here.

What is the sum of the first 1503 square numbers?
Here is the next math problem on our list that we have explained and calculated for you.