Sum of the first 491 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 491 square numbers, you ask? Here we will give you the formula to calculate the first 491 square numbers and then we will show you how to calculate the first 491 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 491 square numbers, we enter n = 491 into our formula to get this:

		491(491 + 1) × (2(491) + 1)
		6

First, calculate each section of the numerator: 491(491 + 1) equals 241572 and (2(491) + 1) equals 983. Therefore, the problem above becomes this:

		241572 × 983
		6

Next, we calculate 241572 times 983 which equals 237465276. Now our problem looks like this:

		237465276
		6

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

237465276 ÷ 6 = 39577546

There you go. The sum of the first 491 square numbers is 39577546.

You may also be interested to know that if you list the first 491 square numbers 1, 2, 9, etc., the 491st square number is 241081.

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