Sum of the first 146 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 146 square numbers, you ask? Here we will give you the formula to calculate the first 146 square numbers and then we will show you how to calculate the first 146 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 146 square numbers, we enter n = 146 into our formula to get this:

		146(146 + 1) × (2(146) + 1)
		6

First, calculate each section of the numerator: 146(146 + 1) equals 21462 and (2(146) + 1) equals 293. Therefore, the problem above becomes this:

		21462 × 293
		6

Next, we calculate 21462 times 293 which equals 6288366. Now our problem looks like this:

		6288366
		6

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

6288366 ÷ 6 = 1048061

There you go. The sum of the first 146 square numbers is 1048061.

You may also be interested to know that if you list the first 146 square numbers 1, 2, 9, etc., the 146th square number is 21316.

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