Sum of the first 88 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 88 square numbers, you ask? Here we will give you the formula to calculate the first 88 square numbers and then we will show you how to calculate the first 88 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 88 square numbers, we enter n = 88 into our formula to get this:

		88(88 + 1) × (2(88) + 1)
		6

First, calculate each section of the numerator: 88(88 + 1) equals 7832 and (2(88) + 1) equals 177. Therefore, the problem above becomes this:

		7832 × 177
		6

Next, we calculate 7832 times 177 which equals 1386264. Now our problem looks like this:

		1386264
		6

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

1386264 ÷ 6 = 231044

There you go. The sum of the first 88 square numbers is 231044.

You may also be interested to know that if you list the first 88 square numbers 1, 2, 9, etc., the 88th square number is 7744.

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