Sum of the first 732 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 732 square numbers, you ask? Here we will give you the formula to calculate the first 732 square numbers and then we will show you how to calculate the first 732 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 732 square numbers, we enter n = 732 into our formula to get this:

		732(732 + 1) × (2(732) + 1)
		6

First, calculate each section of the numerator: 732(732 + 1) equals 536556 and (2(732) + 1) equals 1465. Therefore, the problem above becomes this:

		536556 × 1465
		6

Next, we calculate 536556 times 1465 which equals 786054540. Now our problem looks like this:

		786054540
		6

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

786054540 ÷ 6 = 131009090

There you go. The sum of the first 732 square numbers is 131009090.

You may also be interested to know that if you list the first 732 square numbers 1, 2, 9, etc., the 732nd square number is 535824.

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