Sum of the first 166 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 166 square numbers, you ask? Here we will give you the formula to calculate the first 166 square numbers and then we will show you how to calculate the first 166 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 166 square numbers, we enter n = 166 into our formula to get this:

		166(166 + 1) × (2(166) + 1)
		6

First, calculate each section of the numerator: 166(166 + 1) equals 27722 and (2(166) + 1) equals 333. Therefore, the problem above becomes this:

		27722 × 333
		6

Next, we calculate 27722 times 333 which equals 9231426. Now our problem looks like this:

		9231426
		6

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

9231426 ÷ 6 = 1538571

There you go. The sum of the first 166 square numbers is 1538571.

You may also be interested to know that if you list the first 166 square numbers 1, 2, 9, etc., the 166th square number is 27556.

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What is the sum of the first 167 square numbers?
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