Sum of the first 3977 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 3977 square numbers, you ask? Here we will give you the formula to calculate the first 3977 square numbers and then we will show you how to calculate the first 3977 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 3977 square numbers, we enter n = 3977 into our formula to get this:

		3977(3977 + 1) × (2(3977) + 1)
		6

First, calculate each section of the numerator: 3977(3977 + 1) equals 15820506 and (2(3977) + 1) equals 7955. Therefore, the problem above becomes this:

		15820506 × 7955
		6

Next, we calculate 15820506 times 7955 which equals 125852125230. Now our problem looks like this:

		125852125230
		6

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

125852125230 ÷ 6 = 20975354205

There you go. The sum of the first 3977 square numbers is 20975354205.

You may also be interested to know that if you list the first 3977 square numbers 1, 2, 9, etc., the 3977th square number is 15816529.

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