Sum of the first 221 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 221 square numbers, you ask? Here we will give you the formula to calculate the first 221 square numbers and then we will show you how to calculate the first 221 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 221 square numbers, we enter n = 221 into our formula to get this:

		221(221 + 1) × (2(221) + 1)
		6

First, calculate each section of the numerator: 221(221 + 1) equals 49062 and (2(221) + 1) equals 443. Therefore, the problem above becomes this:

		49062 × 443
		6

Next, we calculate 49062 times 443 which equals 21734466. Now our problem looks like this:

		21734466
		6

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

21734466 ÷ 6 = 3622411

There you go. The sum of the first 221 square numbers is 3622411.

You may also be interested to know that if you list the first 221 square numbers 1, 2, 9, etc., the 221st square number is 48841.

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What is the sum of the first 222 square numbers?
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