Sum of the first 585 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 585 square numbers, you ask? Here we will give you the formula to calculate the first 585 square numbers and then we will show you how to calculate the first 585 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 585 square numbers, we enter n = 585 into our formula to get this:

		585(585 + 1) × (2(585) + 1)
		6

First, calculate each section of the numerator: 585(585 + 1) equals 342810 and (2(585) + 1) equals 1171. Therefore, the problem above becomes this:

		342810 × 1171
		6

Next, we calculate 342810 times 1171 which equals 401430510. Now our problem looks like this:

		401430510
		6

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

401430510 ÷ 6 = 66905085

There you go. The sum of the first 585 square numbers is 66905085.

You may also be interested to know that if you list the first 585 square numbers 1, 2, 9, etc., the 585th square number is 342225.

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