Sum of the first 731 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 731 square numbers, you ask? Here we will give you the formula to calculate the first 731 square numbers and then we will show you how to calculate the first 731 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 731 square numbers, we enter n = 731 into our formula to get this:

		731(731 + 1) × (2(731) + 1)
		6

First, calculate each section of the numerator: 731(731 + 1) equals 535092 and (2(731) + 1) equals 1463. Therefore, the problem above becomes this:

		535092 × 1463
		6

Next, we calculate 535092 times 1463 which equals 782839596. Now our problem looks like this:

		782839596
		6

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

782839596 ÷ 6 = 130473266

There you go. The sum of the first 731 square numbers is 130473266.

You may also be interested to know that if you list the first 731 square numbers 1, 2, 9, etc., the 731st square number is 534361.

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What is the sum of the first 732 square numbers?
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