Sum of the first 1333 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 1333 square numbers, you ask? Here we will give you the formula to calculate the first 1333 square numbers and then we will show you how to calculate the first 1333 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 1333 square numbers, we enter n = 1333 into our formula to get this:

		1333(1333 + 1) × (2(1333) + 1)
		6

First, calculate each section of the numerator: 1333(1333 + 1) equals 1778222 and (2(1333) + 1) equals 2667. Therefore, the problem above becomes this:

		1778222 × 2667
		6

Next, we calculate 1778222 times 2667 which equals 4742518074. Now our problem looks like this:

		4742518074
		6

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

4742518074 ÷ 6 = 790419679

There you go. The sum of the first 1333 square numbers is 790419679.

You may also be interested to know that if you list the first 1333 square numbers 1, 2, 9, etc., the 1333rd square number is 1776889.

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