Sum of the first 1493 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 1493 square numbers, you ask? Here we will give you the formula to calculate the first 1493 square numbers and then we will show you how to calculate the first 1493 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 1493 square numbers, we enter n = 1493 into our formula to get this:

		1493(1493 + 1) × (2(1493) + 1)
		6

First, calculate each section of the numerator: 1493(1493 + 1) equals 2230542 and (2(1493) + 1) equals 2987. Therefore, the problem above becomes this:

		2230542 × 2987
		6

Next, we calculate 2230542 times 2987 which equals 6662628954. Now our problem looks like this:

		6662628954
		6

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

6662628954 ÷ 6 = 1110438159

There you go. The sum of the first 1493 square numbers is 1110438159.

You may also be interested to know that if you list the first 1493 square numbers 1, 2, 9, etc., the 1493rd square number is 2229049.

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