Sum of the first 145 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 145 square numbers, you ask? Here we will give you the formula to calculate the first 145 square numbers and then we will show you how to calculate the first 145 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 145 square numbers, we enter n = 145 into our formula to get this:

		145(145 + 1) × (2(145) + 1)
		6

First, calculate each section of the numerator: 145(145 + 1) equals 21170 and (2(145) + 1) equals 291. Therefore, the problem above becomes this:

		21170 × 291
		6

Next, we calculate 21170 times 291 which equals 6160470. Now our problem looks like this:

		6160470
		6

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

6160470 ÷ 6 = 1026745

There you go. The sum of the first 145 square numbers is 1026745.

You may also be interested to know that if you list the first 145 square numbers 1, 2, 9, etc., the 145th square number is 21025.

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