Sum of the first 988 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 988 square numbers, you ask? Here we will give you the formula to calculate the first 988 square numbers and then we will show you how to calculate the first 988 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 988 square numbers, we enter n = 988 into our formula to get this:

		988(988 + 1) × (2(988) + 1)
		6

First, calculate each section of the numerator: 988(988 + 1) equals 977132 and (2(988) + 1) equals 1977. Therefore, the problem above becomes this:

		977132 × 1977
		6

Next, we calculate 977132 times 1977 which equals 1931789964. Now our problem looks like this:

		1931789964
		6

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

1931789964 ÷ 6 = 321964994

There you go. The sum of the first 988 square numbers is 321964994.

You may also be interested to know that if you list the first 988 square numbers 1, 2, 9, etc., the 988th square number is 976144.

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