Sum of the first 17 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 17 square numbers, you ask? Here we will give you the formula to calculate the first 17 square numbers and then we will show you how to calculate the first 17 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 17 square numbers, we enter n = 17 into our formula to get this:

		17(17 + 1) × (2(17) + 1)
		6

First, calculate each section of the numerator: 17(17 + 1) equals 306 and (2(17) + 1) equals 35. Therefore, the problem above becomes this:

		306 × 35
		6

Next, we calculate 306 times 35 which equals 10710. Now our problem looks like this:

		10710
		6

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

10710 ÷ 6 = 1785

There you go. The sum of the first 17 square numbers is 1785.

You may also be interested to know that if you list the first 17 square numbers 1, 2, 9, etc., the 17th square number is 289.

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