Sum of the first 772 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 772 square numbers, you ask? Here we will give you the formula to calculate the first 772 square numbers and then we will show you how to calculate the first 772 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 772 square numbers, we enter n = 772 into our formula to get this:

		772(772 + 1) × (2(772) + 1)
		6

First, calculate each section of the numerator: 772(772 + 1) equals 596756 and (2(772) + 1) equals 1545. Therefore, the problem above becomes this:

		596756 × 1545
		6

Next, we calculate 596756 times 1545 which equals 921988020. Now our problem looks like this:

		921988020
		6

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

921988020 ÷ 6 = 153664670

There you go. The sum of the first 772 square numbers is 153664670.

You may also be interested to know that if you list the first 772 square numbers 1, 2, 9, etc., the 772nd square number is 595984.

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