Sum of the first 1988 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 1988 square numbers, you ask? Here we will give you the formula to calculate the first 1988 square numbers and then we will show you how to calculate the first 1988 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 1988 square numbers, we enter n = 1988 into our formula to get this:

		1988(1988 + 1) × (2(1988) + 1)
		6

First, calculate each section of the numerator: 1988(1988 + 1) equals 3954132 and (2(1988) + 1) equals 3977. Therefore, the problem above becomes this:

		3954132 × 3977
		6

Next, we calculate 3954132 times 3977 which equals 15725582964. Now our problem looks like this:

		15725582964
		6

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

15725582964 ÷ 6 = 2620930494

There you go. The sum of the first 1988 square numbers is 2620930494.

You may also be interested to know that if you list the first 1988 square numbers 1, 2, 9, etc., the 1988th square number is 3952144.

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