Sum of the first 672 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 672 square numbers, you ask? Here we will give you the formula to calculate the first 672 square numbers and then we will show you how to calculate the first 672 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 672 square numbers, we enter n = 672 into our formula to get this:

		672(672 + 1) × (2(672) + 1)
		6

First, calculate each section of the numerator: 672(672 + 1) equals 452256 and (2(672) + 1) equals 1345. Therefore, the problem above becomes this:

		452256 × 1345
		6

Next, we calculate 452256 times 1345 which equals 608284320. Now our problem looks like this:

		608284320
		6

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

608284320 ÷ 6 = 101380720

There you go. The sum of the first 672 square numbers is 101380720.

You may also be interested to know that if you list the first 672 square numbers 1, 2, 9, etc., the 672nd square number is 451584.

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