Sum of the first 644 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 644 square numbers, you ask? Here we will give you the formula to calculate the first 644 square numbers and then we will show you how to calculate the first 644 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 644 square numbers, we enter n = 644 into our formula to get this:

		644(644 + 1) × (2(644) + 1)
		6

First, calculate each section of the numerator: 644(644 + 1) equals 415380 and (2(644) + 1) equals 1289. Therefore, the problem above becomes this:

		415380 × 1289
		6

Next, we calculate 415380 times 1289 which equals 535424820. Now our problem looks like this:

		535424820
		6

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

535424820 ÷ 6 = 89237470

There you go. The sum of the first 644 square numbers is 89237470.

You may also be interested to know that if you list the first 644 square numbers 1, 2, 9, etc., the 644th square number is 414736.

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