Sum of the first 790 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 790 square numbers, you ask? Here we will give you the formula to calculate the first 790 square numbers and then we will show you how to calculate the first 790 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 790 square numbers, we enter n = 790 into our formula to get this:

		790(790 + 1) × (2(790) + 1)
		6

First, calculate each section of the numerator: 790(790 + 1) equals 624890 and (2(790) + 1) equals 1581. Therefore, the problem above becomes this:

		624890 × 1581
		6

Next, we calculate 624890 times 1581 which equals 987951090. Now our problem looks like this:

		987951090
		6

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

987951090 ÷ 6 = 164658515

There you go. The sum of the first 790 square numbers is 164658515.

You may also be interested to know that if you list the first 790 square numbers 1, 2, 9, etc., the 790th square number is 624100.

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