Sum of the first 760 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 760 square numbers, you ask? Here we will give you the formula to calculate the first 760 square numbers and then we will show you how to calculate the first 760 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 760 square numbers, we enter n = 760 into our formula to get this:

		760(760 + 1) × (2(760) + 1)
		6

First, calculate each section of the numerator: 760(760 + 1) equals 578360 and (2(760) + 1) equals 1521. Therefore, the problem above becomes this:

		578360 × 1521
		6

Next, we calculate 578360 times 1521 which equals 879685560. Now our problem looks like this:

		879685560
		6

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

879685560 ÷ 6 = 146614260

There you go. The sum of the first 760 square numbers is 146614260.

You may also be interested to know that if you list the first 760 square numbers 1, 2, 9, etc., the 760th square number is 577600.

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