Sum of the first 188 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 188 square numbers, you ask? Here we will give you the formula to calculate the first 188 square numbers and then we will show you how to calculate the first 188 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 188 square numbers, we enter n = 188 into our formula to get this:

		188(188 + 1) × (2(188) + 1)
		6

First, calculate each section of the numerator: 188(188 + 1) equals 35532 and (2(188) + 1) equals 377. Therefore, the problem above becomes this:

		35532 × 377
		6

Next, we calculate 35532 times 377 which equals 13395564. Now our problem looks like this:

		13395564
		6

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

13395564 ÷ 6 = 2232594

There you go. The sum of the first 188 square numbers is 2232594.

You may also be interested to know that if you list the first 188 square numbers 1, 2, 9, etc., the 188th square number is 35344.

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