Sum of the first 1266 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 1266 square numbers, you ask? Here we will give you the formula to calculate the first 1266 square numbers and then we will show you how to calculate the first 1266 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 1266 square numbers, we enter n = 1266 into our formula to get this:

		1266(1266 + 1) × (2(1266) + 1)
		6

First, calculate each section of the numerator: 1266(1266 + 1) equals 1604022 and (2(1266) + 1) equals 2533. Therefore, the problem above becomes this:

		1604022 × 2533
		6

Next, we calculate 1604022 times 2533 which equals 4062987726. Now our problem looks like this:

		4062987726
		6

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

4062987726 ÷ 6 = 677164621

There you go. The sum of the first 1266 square numbers is 677164621.

You may also be interested to know that if you list the first 1266 square numbers 1, 2, 9, etc., the 1266th square number is 1602756.

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