Sum of the first 106 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 106 square numbers, you ask? Here we will give you the formula to calculate the first 106 square numbers and then we will show you how to calculate the first 106 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 106 square numbers, we enter n = 106 into our formula to get this:

		106(106 + 1) × (2(106) + 1)
		6

First, calculate each section of the numerator: 106(106 + 1) equals 11342 and (2(106) + 1) equals 213. Therefore, the problem above becomes this:

		11342 × 213
		6

Next, we calculate 11342 times 213 which equals 2415846. Now our problem looks like this:

		2415846
		6

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

2415846 ÷ 6 = 402641

There you go. The sum of the first 106 square numbers is 402641.

You may also be interested to know that if you list the first 106 square numbers 1, 2, 9, etc., the 106th square number is 11236.

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