Sum of the first 711 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 711 square numbers, you ask? Here we will give you the formula to calculate the first 711 square numbers and then we will show you how to calculate the first 711 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 711 square numbers, we enter n = 711 into our formula to get this:

		711(711 + 1) × (2(711) + 1)
		6

First, calculate each section of the numerator: 711(711 + 1) equals 506232 and (2(711) + 1) equals 1423. Therefore, the problem above becomes this:

		506232 × 1423
		6

Next, we calculate 506232 times 1423 which equals 720368136. Now our problem looks like this:

		720368136
		6

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

720368136 ÷ 6 = 120061356

There you go. The sum of the first 711 square numbers is 120061356.

You may also be interested to know that if you list the first 711 square numbers 1, 2, 9, etc., the 711th square number is 505521.

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