Sum of the first 66 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 66 square numbers, you ask? Here we will give you the formula to calculate the first 66 square numbers and then we will show you how to calculate the first 66 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 66 square numbers, we enter n = 66 into our formula to get this:

		66(66 + 1) × (2(66) + 1)
		6

First, calculate each section of the numerator: 66(66 + 1) equals 4422 and (2(66) + 1) equals 133. Therefore, the problem above becomes this:

		4422 × 133
		6

Next, we calculate 4422 times 133 which equals 588126. Now our problem looks like this:

		588126
		6

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

588126 ÷ 6 = 98021

There you go. The sum of the first 66 square numbers is 98021.

You may also be interested to know that if you list the first 66 square numbers 1, 2, 9, etc., the 66th square number is 4356.

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