Sum of the first 1641 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 1641 square numbers, you ask? Here we will give you the formula to calculate the first 1641 square numbers and then we will show you how to calculate the first 1641 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 1641 square numbers, we enter n = 1641 into our formula to get this:

		1641(1641 + 1) × (2(1641) + 1)
		6

First, calculate each section of the numerator: 1641(1641 + 1) equals 2694522 and (2(1641) + 1) equals 3283. Therefore, the problem above becomes this:

		2694522 × 3283
		6

Next, we calculate 2694522 times 3283 which equals 8846115726. Now our problem looks like this:

		8846115726
		6

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

8846115726 ÷ 6 = 1474352621

There you go. The sum of the first 1641 square numbers is 1474352621.

You may also be interested to know that if you list the first 1641 square numbers 1, 2, 9, etc., the 1641st square number is 2692881.

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