Sum of the first 3960 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 3960 square numbers, you ask? Here we will give you the formula to calculate the first 3960 square numbers and then we will show you how to calculate the first 3960 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 3960 square numbers, we enter n = 3960 into our formula to get this:

		3960(3960 + 1) × (2(3960) + 1)
		6

First, calculate each section of the numerator: 3960(3960 + 1) equals 15685560 and (2(3960) + 1) equals 7921. Therefore, the problem above becomes this:

		15685560 × 7921
		6

Next, we calculate 15685560 times 7921 which equals 124245320760. Now our problem looks like this:

		124245320760
		6

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

124245320760 ÷ 6 = 20707553460

There you go. The sum of the first 3960 square numbers is 20707553460.

You may also be interested to know that if you list the first 3960 square numbers 1, 2, 9, etc., the 3960th square number is 15681600.

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