Sum of the first 1987 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 1987 square numbers, you ask? Here we will give you the formula to calculate the first 1987 square numbers and then we will show you how to calculate the first 1987 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 1987 square numbers, we enter n = 1987 into our formula to get this:

		1987(1987 + 1) × (2(1987) + 1)
		6

First, calculate each section of the numerator: 1987(1987 + 1) equals 3950156 and (2(1987) + 1) equals 3975. Therefore, the problem above becomes this:

		3950156 × 3975
		6

Next, we calculate 3950156 times 3975 which equals 15701870100. Now our problem looks like this:

		15701870100
		6

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

15701870100 ÷ 6 = 2616978350

There you go. The sum of the first 1987 square numbers is 2616978350.

You may also be interested to know that if you list the first 1987 square numbers 1, 2, 9, etc., the 1987th square number is 3948169.

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