Sum of the first 167 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 167 square numbers, you ask? Here we will give you the formula to calculate the first 167 square numbers and then we will show you how to calculate the first 167 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 167 square numbers, we enter n = 167 into our formula to get this:

		167(167 + 1) × (2(167) + 1)
		6

First, calculate each section of the numerator: 167(167 + 1) equals 28056 and (2(167) + 1) equals 335. Therefore, the problem above becomes this:

		28056 × 335
		6

Next, we calculate 28056 times 335 which equals 9398760. Now our problem looks like this:

		9398760
		6

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

9398760 ÷ 6 = 1566460

There you go. The sum of the first 167 square numbers is 1566460.

You may also be interested to know that if you list the first 167 square numbers 1, 2, 9, etc., the 167th square number is 27889.

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