Sum of the first 765 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 765 square numbers, you ask? Here we will give you the formula to calculate the first 765 square numbers and then we will show you how to calculate the first 765 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 765 square numbers, we enter n = 765 into our formula to get this:

		765(765 + 1) × (2(765) + 1)
		6

First, calculate each section of the numerator: 765(765 + 1) equals 585990 and (2(765) + 1) equals 1531. Therefore, the problem above becomes this:

		585990 × 1531
		6

Next, we calculate 585990 times 1531 which equals 897150690. Now our problem looks like this:

		897150690
		6

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

897150690 ÷ 6 = 149525115

There you go. The sum of the first 765 square numbers is 149525115.

You may also be interested to know that if you list the first 765 square numbers 1, 2, 9, etc., the 765th square number is 585225.

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