Sum of the first 1967 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 1967 square numbers, you ask? Here we will give you the formula to calculate the first 1967 square numbers and then we will show you how to calculate the first 1967 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 1967 square numbers, we enter n = 1967 into our formula to get this:

		1967(1967 + 1) × (2(1967) + 1)
		6

First, calculate each section of the numerator: 1967(1967 + 1) equals 3871056 and (2(1967) + 1) equals 3935. Therefore, the problem above becomes this:

		3871056 × 3935
		6

Next, we calculate 3871056 times 3935 which equals 15232605360. Now our problem looks like this:

		15232605360
		6

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

15232605360 ÷ 6 = 2538767560

There you go. The sum of the first 1967 square numbers is 2538767560.

You may also be interested to know that if you list the first 1967 square numbers 1, 2, 9, etc., the 1967th square number is 3869089.

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