Sum of the first 1660 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 1660 square numbers, you ask? Here we will give you the formula to calculate the first 1660 square numbers and then we will show you how to calculate the first 1660 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 1660 square numbers, we enter n = 1660 into our formula to get this:

		1660(1660 + 1) × (2(1660) + 1)
		6

First, calculate each section of the numerator: 1660(1660 + 1) equals 2757260 and (2(1660) + 1) equals 3321. Therefore, the problem above becomes this:

		2757260 × 3321
		6

Next, we calculate 2757260 times 3321 which equals 9156860460. Now our problem looks like this:

		9156860460
		6

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

9156860460 ÷ 6 = 1526143410

There you go. The sum of the first 1660 square numbers is 1526143410.

You may also be interested to know that if you list the first 1660 square numbers 1, 2, 9, etc., the 1660th square number is 2755600.

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