Sum of the first 718 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 718 square numbers, you ask? Here we will give you the formula to calculate the first 718 square numbers and then we will show you how to calculate the first 718 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 718 square numbers, we enter n = 718 into our formula to get this:

		718(718 + 1) × (2(718) + 1)
		6

First, calculate each section of the numerator: 718(718 + 1) equals 516242 and (2(718) + 1) equals 1437. Therefore, the problem above becomes this:

		516242 × 1437
		6

Next, we calculate 516242 times 1437 which equals 741839754. Now our problem looks like this:

		741839754
		6

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

741839754 ÷ 6 = 123639959

There you go. The sum of the first 718 square numbers is 123639959.

You may also be interested to know that if you list the first 718 square numbers 1, 2, 9, etc., the 718th square number is 515524.

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