Sum of the first 173 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 173 square numbers, you ask? Here we will give you the formula to calculate the first 173 square numbers and then we will show you how to calculate the first 173 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 173 square numbers, we enter n = 173 into our formula to get this:

		173(173 + 1) × (2(173) + 1)
		6

First, calculate each section of the numerator: 173(173 + 1) equals 30102 and (2(173) + 1) equals 347. Therefore, the problem above becomes this:

		30102 × 347
		6

Next, we calculate 30102 times 347 which equals 10445394. Now our problem looks like this:

		10445394
		6

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

10445394 ÷ 6 = 1740899

There you go. The sum of the first 173 square numbers is 1740899.

You may also be interested to know that if you list the first 173 square numbers 1, 2, 9, etc., the 173rd square number is 29929.

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